measurement of elastic p° photoproduction at hera
TRANSCRIPT
Internat ReportDESY F35D-97-11November 1997
Measurement of Elastic p° Photoproduction at HERA
by
D. Westphal
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Measurement of Elastic p° Photoproduction at HERA
Dissertation
zur Erlangung des Doktorgradesdes Fachbereichs Physikder Universität Hamburg
vorgelegt von
Dirk Westphalaus Wattenscheid
Hamburg1997
Measurement of Elastic p° Photoproduction at HERA
Dissertation
zur Erlangung des Doktorgradesdes Fachbereichs Physikder Universität Hamburg
vorgelegt von
Dirk Westphalaus Watten scheid
Hamburg1997
Gutachter rlcr DisM'rtation: Prof. Dr. R.KlmmerProf. Dr. B.Niiroskü
Gutachter der Disputation: Prof. Dr. R. KlamirrPrüf. Dr. G. Hrin/elnmim
Datum Her Disputation: 15. Oktober 1997
Sprecher dosFachbereichs Physikund Vorsitzender desProniotionsüussclinsses: Prof. Dr. 0. Krmwr
Abstraft
Thr rcaction 7;» -4 p°p (pn -» JT + T ~ ) lins bccn sludied in rp interactions al HERA usingthc ZEUS dctector Tor photon-proton centcr mass encrgirs H\ bctwecn 50 and 100 GcVand for \t\ 05 CJcV1, wliere l is the sqnarc of thc fotir-moincntum transfcr at tlir protonvcrlcx. The. 7r + 7r~ invariant mass Distribution has been irm;stigated äs a fnnction of (. Thcasynirtictry of tlir p° mass sliapr (k'crcascs äs a fiinction of |f|, äs cxprctifl in modcls inwliicli tlic asyninictry is iiscribcd tt> Ihc intrrfrrrnrr of rcsonant and non-rrsonant n+7r~produrtion. Tlir rcsonanl tross srttion has bcrn incasitrcd ns a fnnction of H\ and |/| Theroaction exhihits thc ft-aturcs of a sofl diffractivc proccss, nanicly a wcak cncrgy drpcndcncoof tlir cross scction and a dilfcrrntinl rross scction da/d\t\c r"*'*'. Thc slopc b of thc /d is t r ibdt iun was found to incrcasc äs H'1P intrt'asrs. Thr angular distribntions of thc dccaypions arc analyzrd äs a funrtioii of thc JT^TT" invar iant mass and thc niomcnlniu transfcr |/|and fonnd to l>c consislcnt witli s-chnnncl hclicitv conscrvation.
Zusammenfassung
Die flcaklion 7/1 -t p°p (p° -» TT + ~ ) wurde in rj> \\Vclisclwirkiiiigcn am HERA Spcichcrringmil dem ZEUS Detektor t inlcrsucht . Der kiiicinatisrlic flcrrirh der Messung erstreckt sichiilicr eine Photon-Proton Schwi'rpiinktsenergii1 IV1P zwischen 50 und 100 GcV und |r| < 0.5GcV' im Bftragsqiiiidrat des am Protonvcrlox a itsge t anschien Vicrcrimpiilscs. Die invarianlcJT*JT" Massenvcrteilung wurde als Funktion von ( nntersnclit. Die Asymmetrie der ffl Masscn-vcrU'ihmg vermindert sich als Funkt ion von |(|, in Übereinst immung mit Modellen in denendie Asymmetrie durch eine Intcrferen/. von resonatiter und nicht resonanter n + it~ Produktionbeschrieben wird. Der WirkiingwunTschnit t für die resonante Produktion wurde als Funktionvon H7.,,, und | f | gemessen. Die flenktion zeigt die EigenRchaften eines weichen dilfraktivetiPro/esses. Dies sind eine schwache Encrgieabhängigkeit des VVirkungwjuerschnittes und eindilferentieller \ \ irkungsqucr5chnitt dn/d\l\r exponentiell wie e~t|(| fallt. Ein Anwachsender Steigung b als Funktion von H'.,,, wurde gemessen. Die Winkel Verteilungen der Zer-fallspionen wurden als Funktion der invarianten JT*JT~ Masse und des Impulsübcrtragcs |f|analysiert Dir Verteilungen sind mit S'Kanal-Hclizita'tscrhallung verträglich.
Contents
1 Introduction l
2 The ZEUS Detector at HERA 3
2-1 H E R A Accclrrntor 3
2.2 ZEUS Dctcctor 4
2.2.1 Tracking Drtccturs ß
2.2.2 Calorimctor CAL 8
2.2.3 Smatl Angle Drtrdors 11
2.2.4 Trigger flnd Data Acquis i t io t i System lü
3 Photoproduction at High Energies 17
3.1 cp Intcractions 17
3.2 Rclatiiig rp and 7p Ciws SrrtioiiK 18
3.3 Photon-P m ton Interaclinns l!)
3.3.1 Vt'ctor Meson Dontiicniff Model 20
3.3.2 Ri-ggi1 Phcnc>moni»l)»gy 22
3.3.3 Elast k- (? Pliolo|}rmliicti<in C'niss Sccüun 2ß
3.3.4 Dccfiy Angula r D i s t r i l m l i n n 28
4 Event Selection 33
4.1 The Ela.stic pn PnoloprudMctt im Tiiggt-r 33
4.2 Recotistniction of KiiK-nial i t Variabk-s 37
4.3 Sclccticjn Cuts for Elaslic />" Events 4l
4.3.1 TnickiiigCuts AI
4.3.2 Sclcclion of Eliisl-ic EvciHs 4.)
4.4 St'lcrtion of thc R u n Range 48
5 Monte Carlo Simulation 5l
(.'ONTKNTS
5. l DIPSI 52
5.2 PYT11IA 52
5.3 EPSOFT 53
6 The Acceptance 59
G. l Trigger Accc-ptance 59
G . 1 . 1 Correcting for the CFLT AcL-c|itancc Using Data GO
G.1.2 Tlic AccepUnce Corroclion Melliod 61
G.2 EHk-icncy of tl ic Sclcclion Cuts 66
7 Backgrounds to the Elastic p" Signal 71
7.1 Proton and Electron Deamgas Dackgrnund 71
7.2 Plioloproduction of u) and $ Mesons 72
7.3 Baikground from 7 and Double Dissocialion 74
7.4 Proton Dissocialive p° Production 76
Low Energetic Pions in the ZEUS Calorimeter
8.1 Pions froni f>° Dccays f ind Test Bearn Data . . .
87
87
91
91
92
9.3 Sturly of thc Invariant Mass Distribution 95
9.4 Thc Elastic p° Photoproduct.ion Cross Sektion 106
9.5 The \t\n 113
9.G Decay A t i g u l a r Distribution 120
9 Results
9.1 Corrccliori Procednrc
9.2 Svstrmatic Error . .
10 Conclusions
A List of Hot Calorimeter Cells
B List of Excluiled Runs
C Tables of Data
Bibliography
127
131
133
135
153
List of Figures
2.1 Bird cye's vinv of thc DESY arca. . .
2.2 View of thc ZEUS detcctor in cross scclion
2.3 Vic'W of the ZEUS detcctor in long i t i id ins i l src'tion
2.4 Cross scction of a CTD octant
2.5 Calorimetcr scctions and thcir division in to EMC and I1AC
2.6 Top view of llic outgoing proton brat« Ihre
2.7 Layout of thc PRT1 snntilhilicm coimlers
2.8 Layout of the ZEUS triggcr and da ta arquisit inn System. .
3.1 Schcmalic diagram of rp scaltcring
3.2 Proct'sscs rctated by crossing syimnctry
3.3 Thc p trajcctory
3.4 Prcdictions for thc clastit pn pholo|irodiirliori cross scction.
3.5 The p° deray angles in Üic s-cliannc-l helirily systcm. . . .
4.1 Efficiency of thc FCAL bcarnpipc triggrr nit
4.2 Correlation behvcen the gencraled and thc 1 iccorislnirt . i 'd valncs for the kinematte variables and the decay angles
4.3 Mass ri'Rolution in diffcrc.nl niass bins
4.4 Conversion of P? to |f|
4.5 Invariant mass distributions for p° c; i inl if lalcs and othcr evcnl rhisscs, . . .
4.G Vertcx distribntions in x, y and t, in data
4.7 Energy of llie most cnorgetic ccll in randüin liigRcicd i'vcnts . . . . . .
4.8 Elficicncy of thc cut on the most energctic erII for Mund1 Carlo cvcri ls . . .
4.9 Efficiriicy of the cut on the most cncrgclic ccll for dala
4.10 Nunibcr of events per Imiiinosity
4 .11 The p° signal in ihr 1994 dala
7
9
12
14
15
18
23
24
28
29
38
39
41
42
43
45
4C>
47
48
49
5.1 J U „ t „ - , H"1P, FI and cosO* dis t r ibut ions lor data and Monte Carlo.
usr ÜF nu
5.2 R a t i o data ovrr Monte C'ai lo versus i; für positive j ind negative tuicks.
G . l
0.2
0.3
fi.J
6.5
0 G
G 7
68
G.9
G-10
7.1
7.2
7.3
7.4
7.5
7.6
79
7.1(1
7.11
Monlc Carlo cncrgy sptTlnim nf ibe n* from pn dceays
Tbc fonr trigger rcgions in PCAL .
RCAL triggcr acccptance äs a funct ion of tbc a / imnl l i a l angle $- .
HCAL trtggcr arccptancc äs a f i inr t ion of tbc rail ial distancc R. .
H C A L triggcr acrcptancc äs a f n n r t i o n of t l ic ( rack monicntiim. .
Parameters of tlic RCAL triggcr acceptancc corrcdion promlurc.
)söfl distr ibution in data
56
59
GO
61
62
63
64
66
Acceptancc äs a funclion of M,t,- 67
Acccplancc äs fnnction of H'lpl Pf, cosflj, aml $»,. 68
Acccplancc including snicaring corrections äs a futiction of Ä f w t „ - 69
T T ^ T T " mass distribution for w and <j> backgnniml 73
ll'lp dislribution Tor 7 dissociative backgroiind 74
7r*7r~ mass distribution for 7 dissociativr h;ii'kgroiind 7ö
PRT laggcd cvcnts ovcr all clastic pn cnndidiitcs äs fnnction of thc k inrmat icvariabft 's 77
LPS .r,, distribution 78
P* distribution for cvcnts wi t l i ;i protun in llic LPS 79
Fraction of proton dissociativr cvcnts jis a fiinclion nf Pj 8(1
Thc \ dtlfcrcncc bctwccn data and Monte Cailo for tlic FCAL cncrgy distri-bution 82
LPS r/, spcctnmi for data and Monte Carlo 83
|/| distribution for proton dissocintivc cvcnts 84
flatio of tlic rlastic to proton dissociativc p° cross scction. 85
Hatio of thc cncrgy dcposition in thc calorirnctcr ovcr th<? kinrt ic cncrgy.
Dat io of tlic cncrgy dcposition of positive and negative pions
fl.l
9.2
9.3
91
95
9 G
9.7
Thc di f fcrent ia l tross scction tlo/jt.\f,>,-
Diagrarns of tlic proccssrs considercd in t l ic Sixling inodd. . .
Thc ratio |fl//l| for thc four 11^ intrrvals
Tlic d i f f c r e n t i a l cross scction dn/ilM,,,- in d i f fc rcn l M' lp bins.
The düfrrential cross scction rfn/r/A/..,- i n d i f f e r e n t |/| bins. .
\ H / A \s a fnnct ion o f |/|. . . .
n äs a funclion of |([
89
90
97
101
102
103
UM
10-1
9.R Tlic mass d i s l i i l i i i l i r m in thc mass Hinge i(IO < .U„,„ < 800 McV
9.9 Södtntj niudi'l rrnss srrtion ;w a fnne t ion nf II"1;1. . .
9.10 ParaitH-tfiiizntion and phrnoinrnoloqit'al Sniltiif] Jttixlrl rr».M wtion äs a fiinr-tion of M"1P
9.11 Di l fc ren t tn l cross sectioii <ia/il\t\2 The cnrva tnr r panimctrr c,, «s a f i tn i - t ion of M„,,~
9 1 3 Tlic slopc paratiK'tcr 6„„ äs a funclion of ;U„.„-
9.14 Differential cross section do/d\t\r tlic proccss -y/j -+ p°}i
9.15 Di f fe ren t ia l cross seclion do/ti\t\n \\\,, l i ins
916 Tiic slopc paramctcr bf» äs a funcl ion of U\
9.17 AnioiiMl of skcwing and thc backgroiind äs a fnnrt ion of tosflh
9.18 Amoiinl of skcwing and tlic barkgronnd äs a fmiction of 0,,
9.19 Differential distribntions l/AWV/rfcosffj, and l/iV(/A'/rf^h
9.20 Spin dcnsity n iü t r ix rlcnicnts äs a rnnction of |(|
921 Spin dcnsity matrix clciiicnts äs a fnnetion of .U,,,
1 1 2
I I I
110
115
116
118
119
120
121
122
12'l
I2,'.
10.1 Cross scction für vt-clor nieson proilnclion ;is a f n n r t i o n of 11 \„. 128
List of Tables
4 t Trigger efficicncies in data and Monte Carlo 3G
•12 Parameters dcscribing tlic mass rcsolulion in H'1P bins 40
A 3 Resolution nnd bin widtlis for ihr kincmalk1 variables and thu dccay anglcs. . 40
-l.'l Fniclkm of cvcnls in differcnt cvenl clnsscs for data and Monte Carlo 43
'15 Cnl on thp rnost cncrgrtic ccll. 44
5.1 Monle Carlo gcm-rators nscd in tliis analysis 51
5 2 Monte Carlo rcwcighting paramctcrs 54
(i.l Parameters of thc RCAL triggcr am-ptance rorrci:tioti proccdure 65
7.1 Ratio!; of 7 and doutilr dissociative tross sctlions to the elastic p° CTOSS srction. 75
82
8.1 R a t i o of thc1 cnergy drposition of positive nnd negative pions
7 2 Fraction of cvcnts with n leading proton in tlie LPS, a tag in tlic PRT and atag in FCAL für data and Monte Carlo
89
10(1
1UO
106
108
110
113
9.7 Rrsults of fits to llic dilfcrential cross section do/d\t\7
9 8 Tlic slope paranirlcr bfi in \V^p bins 119
9.9 TliL- mrasurcd spin dciisity matrix Hemrnls 123
9.1 ficsults of Mts to tlic invariant rnass distribiilion
9 2 ßins in U'TP and | f[
9.3 Ri'sults for f i ts to thc invariant mass distr i lnit ion in a rt-stricleii niass ränge.
9.4 Elastic cross section foi 7;» -t p^p
9..'i l iKÜvidua t tontributions to thc systematic nnccrtainty on the cross section.
9.fi Diris in A/,».-
A l List < > f nuisy calorinicter cclls
D. l List of exrlnded rims
132
131
13G
137
138
139
140
C.l Söduig iiinttrl er»-« xvctioti in U'1(l bins (corrcctmn inediod (;i)).
C.2 Södintf modrl rross trclioti in* H1',,, bins (correction rnrlliod ( l i ) )
C.3 Paramctrrization r.ro.ts fcction in \\\ bins (rorrcrlioM nictliod (a ) )
C.4 Parnmctt'rizatton cross sertion in \\'-,v bins (concftioti inetliorl (1)))
C.5 Phrnojiiciwlogical Söiting modrl croxx scction in I1'1P liins (cutTirtioii mcthod
C.G PhrnomcnoloQical Si>dmfj modc.t cross srctioti in I1" lp bins {corrcclioii mcthod
( '>)) ' ' I«
C.7 |O//1| and 11 in |i| bins 142
C.8 b^ in H\ bins obtained froni tlic Södini} modcl cnj.t.'i sccdo» 143
C.9 b^ in Il'1p bins obtained fruin tlic r»i''(i7iir/i^'i;n/i«» rro.ix srctton. , 144
C. 10 bpo in H'1P hins obtahicd froin tlic php.mtmriwIiMjH'al Södmij modrl cin.<ss st'f.tion. Mo
C l l b„ in A/ ,»,- bins 140
C.12 Spin dcnsity matrix elenicnt rjjj in |/| bins 147
C.13Spin dcnsity mat r ix clcmcnt KrfJ in |/| bins 118
C.14 Spin denstty matrix elenimt r f* t in |^| bins 149
C.15 Spin drnsity matr ix rlcmcnl rjjjj in /!/,*„- bins 150
C.IG Spin dcnsity matrix clcinetit Rrfg in A/ (** - bitis 151
C. 17 Spin density matrix element r"l, in Mmt,- bins 152
LtSTOFTMJLES
Chapter l
Introduction
Tlic hadron clcctron ring accclcrator H E R A , located »t DES1»' in Hamburg provides collid-ing brams of elcctrons ' ivith an cncrgy of 27.Ö GcV and proluns with an cncrgy of 820GcV. A big fraction of thc. rp mtcractions, in whicli the cxchangcd foiir-momcntnm betwccnthc incoming and outgoing clcctron is smnll, havc an Interpretation äs plioton proton (jjt)intcraclions. Elastic photoproduction of veclor nicsons, 7;» -4 \ is a spcrial kind t)f suchphotoproduction rcactions. It h äs bccn studicd in lixcd targct expcrimcnts at plioton-prolimccntcr of mass cncrgics up to H'1P Ä 20 GcV and at HERA for U'1P n p to approximatcly 200GcV. Elastic photoproductiun «f p°, tu and <£ ilicsoiis at liigli t-ncrgics cxliilnls tlir fcattirrsof a sofl diffraclivc proccss, nanicly a «rak rnrrg\ di-pt-tulrntc of tlir cross srclion and adcprndcncc on t, t l i r sqnarcd foiir-nioinc'iitnni traiisfcrrrd ;il ihr pioton vt-rtcx, wliicb isnppro.xitnatcly t'xponcntial at sinall |f|. Sucti a» rncrgy anil / <ln|)cinlctH'(' , tvpi ta l of claslichadron-liadron intcractions, an- consisu-nt w i t h ihr cxpfrlations t > f ihr. Vculnr DuniinaiiccModel (VOM) in which thc plioton is assnmcd to ( l i ic tna tc in tu a vrclor nicson bcforc in-tcracling with thc proton.Thc vcctor iticson is obscrvcd to rrtain thc hclicity of tht- phototi(s-dianncl hclicity conscrvatinn SCHC).Elaslic photoproduction of/>° nn'sons lins alrcady bccn olisrrvwi ai HERA |l 111, "jl], howcvcrmany aspccts of clastic p° photoproduction at targc- H fTP rcinain to bc clarilicd. Arnong thcni,tbc U'TP dcpcndcncc of thc* cross scrlion, thc H''1P dcpcndcncc < > f ihr t slopc, thc origin of tlicasynimctry of thc p° rcsonancc shapc and ihc cxtcitt to wliirh tlir l ir l ici ly of thc plioton istransfcrrcd to thc ffl. In gcncral, clastic pliotoproduction of p° nicsons at. HERA inay olfcra nicans of invcstigating thc tiatiirc of thc soft hadionic inti-raclion äs well äs ihr hadronicfcaturcs of thc plioton.
This thcsis iltiscrilics a nicasurcnicnt of clastic p° plioloproducltun using data collcctcd in1994 by thc ZEUS cxpcrinicnt on thc rcjirlion rj> -4 rpnp (p" —* T T ^ T T " ) nt sinall phototivirlualitics(^! <,4 GcV (thc incdian QJ is about II)"1 GcV2) In t Ins mcasurcniciil ilic h ' t ia lstatt1 clcctron was not dctcctcd. Thc scattcrcd proton was incasurcd only for a subsampk-of Lhc data. Thc relevant k incnia t ic ( |iiantitics wcre dclcrnt tncd froni ihc nieasnrcd thrce-rnoinenta of (hc pn dccay products, assiitning tha t thcy werc pions. With rcspcct to thcpublishcd ZEL'S data [Ilü|, thc prcscnt rcsiilts fraturcs hirger stalistics, n wider W1P ranRcand smallcr syslctnatic unccrt aintics. Thc kincniatic ränge of Ihr measureiiicnt was rcstricl edto 50 < WT, < 100 GcV and |,'| < 0.5 GcV1.
'Since 1994 posilrons arc slorH in HERA itistead of plrrtrons Thp lot m plrrlron will hf fnrtlier uspila f-ptterie name for Hertrons anrf positrons
The tlicsis is organi/cil iis folbws. Tlmsc coiiipmH'iils of dir ZEl'S dctcrtoi relevant fnr diis
analysis nie intiodiurd in rhaptrr 2. Cliaptci 1 runtains a slmrt introdnrliori tu dir pliysirs
of pliotoii-ptotoii rcarlimis ;i[ HERA cspcrirdK tu rhslir />" plioloprodm'tion. Tlic online
IrJRKcr ;im! olllitic cvciit solection ;IK well äs tlic rcconstrnrtion of tlic kitictnatic variaMrs
iirc prrsciitcii in tliuptcr -1. Chaptt-r Ti conlfiiiis ;i ilrMTiplioii of tho Muntc Cfirlo siiiiiihition
progiiiins lisi'd in tliis jinalysis. In rhaplcr Ct tlir iircr|i(;iiicc of ihr ZEL'S dclcttor fnr rliistic
/i° pliolo]ii(Kiurlioii is prcscntrci, anrt Mir inrllind nscd to dclcrniinr dir riilorimctrr triggcr
cllicirnty froni llii1 ilata is introdiiccd Chaptcr 7 is drdicatrd to tlic ilrlcnnination i>f tlu-
li;ickgnnnnls l o llic claslic p° signal. Tlic higRrst liarkgroiititl riintrilxition is givcn liy proton
dissociativr /)° prorlnrtion, which was dclcriTiinnl l»y a siibsamplr oftln- (tata in wliicli clastic
i'M-iits \\vrr nnainliignoiisly sclcctrd In cliaplcr 8 tlic rrsptMisc of ihr caliniinctcr fnr lln-
ff drciiy pions is prcsriUc'd and rliaplor 9 snminari/cs tlic ri'snlts obtaineH in tliis tlicsjs.
Tlirv rnvcr a slndy of tlir fi° niass asymmrtry, a tncasuri'inriit of tlir nicrgy depcndcncr of
dir cross si-tlinii and die t slopc and n slndy nf tlic p° drcay angnlar distrihutions. Finally
coiiclusinns an* givcn in cliaptrr 10.
Chapter 2
The ZEUS Detector at HERA
2.1 HERA Accelerator
Tlit* Hadron Elektron Ring Anlage HERA, loratcd at DF.SY in Hamburg rnnsisls nf two
storagc rings, 6.3 km in ciicnnifcrcncc in a tiinticl 10-30 m Underground (fiRinc 2.1). In
HERA clixtrons ' of 27.5 GcV cncrgy and proIons of 820 Gi-V cncrgy cirnilatc in opposilc
dircction. Tlic bcanis collidr at /cro crossing angle in tlic two intrniction rrginns nordi (N)
am! sou t h (S), whirh arc otcupird by ttic ZEUS (S) and Hl (N) cxpciimcnl. In tlicst- two
cxpcrimcnts clcctron i>roton intcractionsat a centcr ofni;'sso]icrg\ ,/s ss,100 GcV arrstndk'd
Fignrr 2.1: Binl cyc's vicw of llic DESY arra in Hamburg. Tlic daslicd lincs imlicatc tlic
Incation of tlic PETRA and HERA storagc rings.
1994 posilrnti^ atc slor«! in H KR A iiiMPfii! of rlrrlions "Die (crni rlfrltiiii »ill lio finllipf
naine for plorlnnis nnrl [irisiltoiis.
-2. Tl,<- ZKUfi D.-l^to, at H/dM
since 1992. The two rcmaining halls are uscd Ity tlu1 cxpei imcnls HERMES (cast hall O)and HER.A-B (wesl hall \V). These two rxperinic.nl s make nse of tlic polarizcd clcctron bcani(HERMES) or t l i c proton brnm (HERA-B) ouly. HERMES uses tlic longi tndinal ly polarimlelcclron bcam in tlic (.'äst liall to study the spin structiirc of ptotons and ncntrons. HERAis tlic world's lirst storagc ring in which thc natnral Iransvcrse clectron polarizntimi caiisedl iy Synchrotron radiatioti in thc dipolc magncts [105] is rotatcd to proviilr longitiiclinaltypohiri/ed elcclrons. HERMES st;irled opcrntion in 1995. Tlie D-pliysifs cxperimcnt HERA-ß is nirrent ly nnder Installation.
Elcctrons and protons are accclcratcd in a thain of linear and circular accclcralors lucatcd011 I l io DESV sitc bcforo thcy arp injccted at an cricrgy of 12 GcV (clcctrons) and <!0 GrV(protons) into HERA. In HERA botli particlc spccics arc thcn accclcratrd to tlu-ir collisionciu' iRk'R. Tlic maximal cncrgy of protons in HERA is givcn by tlic maximal avnilabtr mag-n i - t i c fit'ld. To störe protons at 820 GcV in die circiirnfcrcnrc of H E R A , tlic supcr-conductingH E R A niiigncts providc a magnctic ficld of -1.68 T. In contrast, tlic ficld rcqnircd to storo 30G''\ clcctrons can bc accoiiiplislird Ity convcntional mngncls. Tlic maximal elcctron cnrrgyis givon by ihc avaüablc radio frcquency powcr nrccssary to compcnsatc Tor llic losscs ducto Synchrotron radiation.
Tlir bcams of protons and t-lrctrons arc bnnrlicd and cacli of tlie HERA rings is capabk-of storing 220 bunchcs of particlcs. Tims flettroiis and protons mcct cvcry 90 ns in tlicexpmments Hl and ZEUS. In 1994 tlic HERA rings wen- fillcd witb 153 colliditig bundics.Tbc ciirrrnls rcaclicd 30 in A in casc of clcctrons (dcsign 58 mA) and 50 mA for protons(dosign 1G3 mA). The highcst obscrvcd himinosity was 5M030 cm"' s~'.
2.2 ZEUS Detector
ZEUS is a mnlti pnrposc dctcctor bui l t and oprrafcd by a collaboration of 450 pliysicislsfroni 50 Institutes of 12 countrirs. An ovcrvicw of thc detcclor is given in fignrc 2.2 andfigurc 2.3. ZEUS is asynimetric in tlic proton dircction bi-causc; of thr boosl of llic clcctronproton center of mass.
Tlic coordinatc System used tliroitgliont tliis tlicsis is thc right handcd ZEUS cnordinatcSystem dcfincd äs follows. Thc z-axis lies in the dircction of tlic proton bcam, thc x-;ixispoints hori/,ontally towards thc center of tlir HERA ring and thc y-axis points upvvards. Thepolar angle 6 is mr-asiired witli rcspcet to llic positive / direction and t ho a/ imutl ial angle 4>is nu'asiircd around z relative to tlic positive x direetion.
Cliargcd partielcs are tratkcd in ZEUS by thc inner tracking systcm comprising a vcrtrxilctcctor (VXD) and a central tracking dütcctur (CTD). Botli detectors an- cylindrical driftchnnibers. Thc tracking System is coniplctcd by planar drif t chambers in the forward (pro-lon) and rear (elcctron) direttions plus t ransi t ion radiation detectors in thc forward region.A Ü i i n super contlucting solenoid surrounds the inner tracking detectors and produccs amagnctic field of 1.43 T, allowjng nioinciituni incasiirnnonts for chargcd partick's. ThcCracking devices are snrroundod by a high rcsohition calorimetcr. Thc calorinietcr consislsof ihrer parls covering dilferent regions of the polar angle (forward (FCAL), barrcl (BC'AL)and rear (RCAL)) . Each pari is dividcd in dcptli into an clectniinagnctic and a hadroniccompunciit.. Thc magnrtizcd iron yokc siirroiimüng thc ralorimeler is instrumented for tlicuse ;is a backing caloriinclcr (BAC) and iiinon detector (BMUO/I, R M U O / l ) .
ZJ'JU.S l),-t,;-t„l
Overview o! the ZEUS Deleclor, { cross sedton )
-5m 0 i m
Fignre 2.2: \'iew »f ihr ZEUS ddrctoi in cross sc< tion.
W m 0 -'j mFignrc 2.3: View of thc ZEUS dclrclor in I m i g i l i i d i i u i l scclion
In llir forwj i rd d i r r r l ion , irun luroids and t racking ch.imbcrs itnprove Ibe iiiiion detcction(FMtON). The proIons ;unl nciitrons cmitlcd undcr vcry small anglcs in tlic forward di-riTtion ;trc mca.snn'd in the Irading proton spei-tronictcr (LPS) and thc forward nciitronralorimelcr (FN'C) inshdled in tlic HERA tnnncl bi-twcen 24 and 101 ni. Slighlly largcr sral-Icring anglcs arr covcred hy tlic prolon r rmnnnt laggcr (PRT) mstallcd bcliind tlic FCALat /=5 in. In (hc backward dircction photon and clcclron dctcctors dose to the beanipipcscrvc äs a lii ininnsity monitor (LUMI). In ordcr to reducc thc roiitaminaMon of tlic datawil l i |>rotoii licamgas rvciits, ZEUS is eqmppcd w j t h background delectois in particillar tlicvcto wall (VETO), t l ic Cö countcr and tlic smatl angle rcar tracking detcctor (SRTD).
In t l ic following tlmsc dctrctor coniponcnts, which arc uscd in this analysis arc shortly intro-dnccd. A dctaited dcscription of al l ZEUS dctcctor coniponrnts tan bc found clscwhcrc |1U7).
2.2.1 Tracking Detectors
Thc Iracking dcvicrs relevant to this analysis arc tlic vrrtcx dctcctor (VXD), thc ccntralt rarking dctcctor {CTD) anH thc roar trncking dctcttor (RTD)
Vertex Detector VXD
Thc VXD is a cylindrical, liigli prrcision tlrift cliamhcr |")| sitnatcd hctwccn the ontcr radinsof tlic bcatn pipL' and t IM: inner wall of thr CTD. l! has an inner radins of 9,9 cm and an outcrradius of 15.9 cm. Thc cliambcr is opcralcd w i t l i Dimcthyl-Elhan (DME) at atmosphcricpressurc. GOOO wircs, 1.59 m in Irnglh, run parallel to tho ^-axis and are organizcd in 120cclls eacli containitig 12 scnsc wircs. Thc VXD covcrs t l ie angular rcgioii 8.6a < ff < 165°.A spatial resolntion in rtfr of 50 ;mi in thc ccntral regio» of a ccll and 150 /<ni ncar tlic ccllcdgcs is acliicvrd.
Central Tracking Detector CTD
Tlic OTD [-H] is a cylindrical drif t clianibpr surrounding tlic VXD with a Icngth of 240 cm,;in inner diamctcr of 32.4 cm and an outcr diarncter of 164.8 cm. Its aclive Icngth is 2 mrorrrsponding to a angular coveragc of 15" < 0 < 1C40. The ehanibcr is fillcd with a gasmixturc of Ar:COi:CiH6 (9!):8:2}. Thc CTD consists of 72 cylindrical drift laycrs arrangcdi n t n 9 nupr.rlayprx (lignrc 2.4). Thc wircs witliin a supcrlaycr an1 arrangcd aztniuthally incclls, cacli containii ig 8 scnsc wircs. In total thc CTD is cquippcd with 4608 scnsc wircs.Thc odd numbcred snpcrlayers havo wircs striing parallel to thc Z-HXJS (axial laycrs) whilcthe four evcn nnnibcrrd stcrco laycrs arc tiltcd by sterco anglcs hetwccn -5.53° and +5.62".Tlic scnsc wircs in supcrlayer I and altcrnate wires in snpcrhiycr 3 and 5 tiavc an additionalrcndonl systcrn which providcs a fast Determination of thc track 7. coordinatc by measuringIhr differencc in arrival tinic of signals froni both cnds of thc cliamhcr. This Information isusc-d iis inpnt lo the trigger and discriininates agninst cvcnts ranscd by npstrcarn bcamgasintcractions. Tlic CTD achicvcd in 1994 a spatial resolutioii in r* of 191 (im |7G] and a 7.resolntion of thc 7,-by-timing systcni of 3.3 cm.
2.2. ZKUS
n"f/t
Figur« 2.4: The arrangcmcnt of wircs in one octant of thc CTD. Sense wircs arc indicatcdby largrr dots.
Rear Tracking Detectors RTD
Thc RTD [15] is a planar drif t cliambcr cxtcnding the ZEUS inner tracking System in ihrrcar dircctiort It consists of tlircc laycrs of drift colls perpeiidicnlar lo thc bcam axis withwirc oricntations at 0", +60° and -60° witli rcspcct to the horizontal . Thc RTD covcrs polaranglcs bctwccn 1GI)° and 170°. Thc six sense. wircs in «ich ccll arc scpfirated by 7 mm andaltcrnate wircs are. staggcml by 300 /mi with rcspcct to llir potcntial wircs to n.-solvc thcIcft righl ambiguitv. Dnring tlic 1994 data taking period thc RTD was opcratcd in ZEUSfor thc first linic. It took data in 80% of thc luminosity uscd in this analysis Thc 20% lu-minosity takcn withoul tlie RTD is acconntcd for in the Monte Carlo Simulation (scction 5)by cxcluding the RTD from tlic track rcconstruction in 20% of tlic Monte Citrlo cvcnts. Fortlip 1994 data thc RTD singlc wirc cfficiency was 91.5% and tlie single wirr spatinl resolntion240-300 f tm |83j. Thc tlircc RTD laycrs providc threc indcpendent stcnx) views of a track de-nient. So thc RTD i n form;» t ton nlonc allows to rcconstruct a thrcc dimcnsional track elcmcnt.
Track and Vertex Reconstruction
Thc VCTRAK |5C| track h'nding program rccognizcs trajcrtories in tlie CTD, i-xtcnds thcminto thc VXD, fits ihcm and thcn cstinialcs thr primary vcrtcx Track scgmi'iits found inthc RTD arc nscd äs an inpnt to thp program äs well. Thc paMcrn rccngnitinti algorithmbcgins by looking for a trai'k sced in an outcr pari, of thc CTD A si-cd can cithcr consistof thrcc CTD hits frtmi an axial supcrlaycr or of a thrcc dimcnsional Inirk scginent in thcDTD plus a singlc axial CTD hil from supcrlaycr 3 or 1. Given a Irack smt, thc trajcctoryis cxtrapolated inward w j t h incrcasing prccision äs more axial h i t s arc assigncd to the trark.
2. Tlic X / v f ' S
Thc resultmg trajectoiy forms a ciiclr in t l ic \\, which is iiscd für tlir x-by-liiningand stcrco p a l t e i n recognition. Tlic / -by- t i tn ing and Stereo h i t s iiiatching tliis trajcctory areuscd to provide / Information about llic Irack. Evcntually cvcry Irack candidatc nuist havethree-dimcn.sional Information. An a t tumpt is madc to pick up hits in tli« VXD. Thc longesttracks arr fonnd h'rst, thcn slightly shortcr ones.
After correcting thc drif t distancc for varions systematk cffccts tlic track candidates arefided (o a fivc paramctcr hclix modcl. A niomentum is first cstiniatcd by using tlic slopeand curvaturc providcd by tho pattcrn rccognition. A trajcctory is cstablishcd by swimmingtlirongli thc niagnctic ficldslarting froin thc vic in i ty of thc iniicrinost uscd hit and proceedtngoutward äs far äs nccessary. This swnm trajectory is uscd lo calculatc thc hit rcsiduals äsweil as thc derivatives of tlic rcsidiials wi th rcspect to Ihc hrlix parametcr. Finally thctrajectory and its covarinncc matrix arc traiisportcd imvard to the z-axis.
Tbc primary evctit vrrtex is found in a threc s tage proccdtirc. First trajectories incompatiblcwith thc bcam-linc arc rcmovcd. The rcmaining tracks arc uscd for an in i t ia l cstimatc of thcvcrtcx as the weigbtcd ccnter of gravity. Tracks with thc maximum contribiition to thc x*arc discardcd onc by one unti l thc fit quality is acccptable. In a final stsgc a füll vcrtcx fitis performed which not only solvcs tlir final vcrtcx position but simultaneously re-evaluatcsthc tratk paramcters constrained to this vertcx. Thc direction and curvaturc of tho tracksat thc vcrtcx, rescaled to thc curvaturc bcfore thc vcrtcx fit, are uscd to detcrmine thc trackmomcntum at the vertcx.
Thc rcsolution in transvcrsc momentum rcachcd for füll tracks in thc CTD and VXD iso(Pr)/Pr ~ \/(0.005 PT-)3 + (0.01G)2 whcrc Pr is in GcV.
2.2.2 Calorimeter CAL
Thc ZEUS calorimctcr (G, 30, 14| is a high rcsolution s;tmpling calorimctcr. It consists ofalternating laycrs of dcplctcd u ran ium (3.3 mm th ick) and plastic scintillator (2.C mm thick)wilh onc radiation Icngth sampling. Tlic light is cotlcctcd via wavclength shifter plates andrcad out by photomultiplicr tubcs. Thc ZEUS calorimctcr has cqual rcsponsc to electronsand hadrons, i.e. H is a contpcnsating calorimctcr. Compcnsation is achieved by choosingthc correct fraction of absorbcr to rcndout nialcrial.
Tlic calorimctcr surrounds thc inner tracking System and consists of threc parts: thc For wardcalorimcter (FCAL) in proton direction, the rear calorimctcr (RCAL) in clcctron dircctionand the barrcl calorimcter (DCAL) surrounding thc ccntral rcgion (figurc 2.5). The FCALcovcrs the ränge 2-2° < 0 < 39.9°, thc BCAL thc ränge 36.7° < ß < 129.1° and thc RCALtlie ränge 128 1° < 8 < 176.5". Thc forward and rcar calorimctcr are bui l t out of 24 modulcsräch, wi th maximum attive dimensions of I G m hcight, 0.2 m width and 1.52 m (FCAL)or 0.90 m (RCAL) depth. In thc ccnter of thc FCAL and RCAL scction an arca of 20x20cm2 is Icft out for the beam pipc. The barrel calorimetcr is build out of 32 wedgc sliapcdmodulcs with approximatc dimensions of 3x0.5x1.7 m3.
The modules are subdividcd transvcrscly into towcrs and longitudinally into onc clcctromag-nctic scction (EMC) and onc (in PCAL) or t wo (in FCAL and BCAL) hadronic sections.Thc EMC sections havc a depth of ~25 radial ion tcnglhs, ,V0, enough to fully contain eh'c-tromagnetic showcrs. Thc depth of thc EMC is eqiiivalent to one nuclear i i i t i ' raclioii lenglhAr for hadrons. The HAC sections vary in deptti from G A0, for hadrons in thc fonvanl dircc-( i n i ) (o 3 A0 in llie rcar. AH caloriiiictt:r (owers arc non iirojeclivc excepl l l ic DCAL lowrrs,
2.2 ZKUS l)i-l,;-tn,
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\
HAC 3l* .
Figurc 2.5: Thc dirfcrent calorimctcr sections and t l i c i r rli\-ision in t» EMC and HAC cclfs.
which arc projcctive in a / imn tha l angle 0. Tlic EMC tmvcrs of BCAL are als«) projectivc inpolar angle B. Eacli barrc! calorimctcr inndulr is rotalcd by 2.r»° cluckwisr in tlic a/imirtlialplane around an axis parallel to thc /-. axis. This rotalion assnrcs tha l llic wavcli-ng(h s l i i f lcrdo not point to the beam axis.
A scction of a towcr is callcd a teil; earh ccll is \-icwcd by twu pho tnnml t ip l i c r ttilics. Tticccll sizc in tlie EMC sections are 5x20 cm' in FCAL and DCAL, 10x20 cm2 in RCAL and20x20 rm* in all HAC sections. In tlie rcgion whrre FCAL and RCAL as srcn from thcnominal intcraction point arc hiddcn behind thc barrcl, Hie EMC segmcnUition is idmtiralto thc onc in the HAC, namely 20x20 cm2 (thcse cells are callcd HACO cells) Each IIACrespectively EMC ccll is rcad out by plastic wavelcnglli shif ler plalcs, at tachnl 011 oppositcsidcs of the ccll, lightguides anrt altaclied photomultiplicr tnbes (PMT).
Thc pipclined calorimeti-r rcadoiit clectionics covcrs a big dynaniic ränge-, altowing ]>rccisccnergy measurcnieiit from MIPS (300 McV cqnivalait cner^v in EMC cells of FCAL) uj ito thc highes t cxpcclcd signals (^400 GcV in ind iv tdua l cells of FCAL), by Spli t t ing tliePMT signals in a high and low gain palh. Tlie fast rrsponsc (iinr of tlu- plastif scinlil-lator togethcr w i t h tlic rcadmit clcctronics altows lo measnrc ihr ( i i n i n R „f ;1 siptial in acalorimetcr cclt wi lh a resolnlion of Icss than l ns für cnergy dcposits grraler than 4.5GrV. The cnergy lesolution l inder lest beam conditions w i thon t inac t ivc n i i i l e r i a l in frontis n{E)/E = 0.18/y£[GrV|e0.01 for elcclrons and n ( E } / E - ().3,V/^[GeV] ©0.02 forha r ln ins .
11) Ct<;<l>ü-i 2. T/IC ZKUS Orlrr(..r nt
Tbc Performance, cncrgy and (ime calibration of Mir calorimctcr an1 continunnsly monitorcdiising pcdcslal triggers, charge and lighl injection äs well äs tlic nranium ladioactivitv. Tlirn r a r i i i i n i mdioactivity can bc uscd äs a Standard tocal ibra te tlic calorimclcr with an acciiracyofaboul 1%.
Tlir noisc of tlic calorimcter is npproxinmtcly lä McV for clectroinagnctic and 25 McV forhadronic teils, doniinaled by ihc uranium radioartivity.
Calorimeter First Level Trigger CFLT
Thc CFLT 1100] providos triggcr data Tor a global first Icvcl triggcr (GFLT) dccision 5/is aftcrcacli brain trossing, occurrhig cvcry 9G ns. Tlir charges froni thc 128C4 photomnltipliers oftlic C'AL (irr snmincd in 1792 triggcr towcr pulsehcights which arc digitized by flash ADC's.Tlic digilal valncs arc linearizcd, storcd and uscd Tor sums and pattcrn tcsts. Energy sumsan* transfcrcd to tlic GFLT fbr cacli crossing 2 fts after thc crossing occiircd. Thc decisionsarc derivcd in a pipclincd fashion cvcry 96 ns.
Triggcr tuwers consist of a block of fonr (FCAL and BCAL) or two (RCAL) EMC cclls, andlliosc HAC cells tliat lic most projcctivc bdiind thc EMC cells. Thus rarh triggcr towcrhas a sizc of 20x20 cm1 and is dividcd into an clcctroniagnctic and a hadronic scction.Thc encrgy sums corrcsponding to thc 896 triggcr towers are fornicd in triggcr sinn cards.Trigger towcrs arc organizcd into sixtccn 7x8 Iriggcr rcgions; RCAL and FCAL consist offour triggcr regions each and BCAL of ciglit. Thc analog signals froin thr triggcr suni eards,are transfcrcd to triggcr cncorlcr cards, whicli digitizc thc Information cvcry 90 ns by two 8bil (lash ADC's w i l l i high and Iow gain .
After digi t i /at ion thc triggcr cncodcr cards l i r iear ize , pcdcslal corrcct and mro snpprcsstlic signals, n iak ing use of nicmory looktip tablcs. C'jililtration constants are reloaded intotlic liKiknp tablcs. Thc calibration is aceornplislicd witli tlic eharge injrction systcni of thrCAL rcadout. The diargc injcetors arc fircd and thc piilsrhcights for thc trigger towcrs arei n d i v i d u a l l y coniparcd againsl tlicir cxpcetcd valucs. Thc resolut Ion of the digitizcd triggcrcncrgies is 49 McV (high gain), I G GeV (Iow gain FCAL) or 0.39 GeV (Iow gain fiCAL andBCAL) givtng a dynaniic rangr up to 400 GeV. Etiergies brlow a Iow tlircshold, prcscntlyal 4G'( McV arc sct to zero (zcro suppression). The corrccted energies are iTiiiltiplicd bygeomctrir fattors to calculatc clcetromagnetie and hadronic total cncrgy £(0,aii transverscencrgy E/, E, and Ey using again lookup tablcs. It is also testcd wliethcr tlu- cncrgvdcposition in a trigger towcr is consistent wit l i an clcetron candidatc, a miii inuim ionizingpartirlc or a qnict towcr and i t is ddcrminrd whkh of six thrcshold values (3 bit) issurpasscdby llic signal.
Adder cards combinc thc infonnat ion ( E l ( l l f i , ET, Ex and Ey) from thc trigger o n coder cardsfor a singlc triggcr region. It also applics pattern rccognition algorithtns to idcntify isolatrdi'lectrons nnr t nnions in a singlc trigger region and caleulatcs the energy sums 011 a 3 bitsc.nlc. The adder cards send thcir information to the CFLT proccssor.
Thc CFLT processor ealculates the total ET, niissing transverse energy E-/-, elcctroniagncticand hadronic energy, comparcs region boundaries to calculatc the number of isolated rlcc-truns and nnions and computcs regional EN'IC, HAC and total energies, pnr t icular ly aroundthc bcani pipc region. Thc suinmary of this information is transmittcd to the GFLT for caehcrossing. Thc quant i t ics uscd in thc triggcr for clastic />° pliotuproductictn are discussed insection 4.1.
2.2. Zl-;i!S Drlntoi
2.2.3 Small Angle Detectors
Luminosity Detectors LUMI
The lumhtosity is nicasnred by dctccting Rreinsstrahliiiig photons froni (he proeess c\> -* c~^p.The cross section for this process is known lo high ncciiracy froin QED givcn by the Delhc-Hcitlcr fomiula. Thns by acctirately dclcnnining llie rate of Detlie-Heitler photons abovc agiven energy thrcshold a prccise dcteriiiinalion of the l inninosity is possible.
Brcmsstrahlung photons, scattered at an angle less than 0.5 mrad, are deteetcd by a Icudscinttllator Calorimeter |7, 84] posilioncd in rlectron bcani direction at a <li.slance of 107m from tlic inlcraction point. Thc calorinieter is 23 radhi t ion IcngtliP (A'0) deep and Iiasa position deteetor inserted aftcr 4 .V0. Thc calorinn'lcr is shietdcd against Synchrotronradiation by a carbon f i l ter (1.5 A'o) plaecd at /,=-103 m and Icad sliielding (l A'o)- The
calorinictcr has a resolulion of a(E)/E - t).18/i/£T[{7r\"],
Breinsstralilnng of clectrons on rest gas niolecnles has ihc snnie experimcntal s ignatnre äs rj»Brcnisstrahlung. To subtract this background, MIC cvciit rate for nnpuircd (p i lo t ) clcctronbtinthcs is also dctermined. This bnckgroiind rate is sutlrd by thc tiirrent of partieles intliosc bnnches witli rcspcct to thc bunclies (hat par t ie ipate in r;i collisions and subtractcd.
An additional calorimetcr at a popition of /=-3ö m deterts clec trons scallcrcd a! sniall an-gles. Electrons froin Ihr interartion point that an- bclow noni ina l beam enrrgy are dcflcctcdby dipole and quadrupolc magnets onto die clcctron caloi i incler . Tlic acccptaiice of theelcctron calorimetcr in encrgy is thcrcforc resinrlcd lo E = (5.2 - 21.2 GeV [73].
Leading Proton Spectrometer LPS
Tlie LPS detects chargcd partieles scattcred nt sm;tll anglcs and earrying a s n b s l a n t i a l frac-tion, .r/,, of the incoming proton i i iontentnm. These partieles rcmain in l l ie bcani pip'1 andtlicir Irajcctories arc nicasurcd by (\m of posilion sensitive silieon micro-slrip deteetorsvcry dose to thc proton bcam. Tlie track deHcction iiiflnced by the magncls in th'1 protonbcam line is uscd for thc momentiim analysis <>f Ihc scatlercd protoit.
Thc LPS [114] cotisists of six detcctor stations. S l t o S(i of whicli in 199-i only S-1 lo Sfi wen-eqiiipped. Only tlicse stations wi l l bc dcscribcd in tlic lol lowing. The stf i t ions arc jilaccdalong thc bcam linc at z=G3.0 m (S-l), 81.2 in (So) and 9IMI m (SG) respcctivcly. Eadi oftlicse stations cotisists of two hatvcs, cacli half nmta in ing an as-scnilily of six planes of silieonmicro-sttip dctectors iiioiinted on a mobile arm F.ach assembly has two planes wilh vcrlicalStrips, two planes at -H5° and two planes a l -•15° witli rcspert in the vcrtical. Thns thcpartick- trajeclory is measurcd in three d i l fc t r i i t projcctions in cacli assembly. Thc pitdiis 115 ftm for planes witli vertical Strips and 8l /im for t l ie planes witl i ±45" strips. Thcdistancc in / betwccn ncighboring planes is l mm.
The deteetor planes arc inserted in the beam pipc by mcans n f » stccl cylimlcr w i t l i im opetinid away fi'om the bcam and Ihc olhcr cm! closed (nomni i pol) . Thc silieon dclcrtors areinserted from the opcn end and Ihc wliole cyl indcr is inscrlcd in io llie bcani pipc. Tlic planesin thc two lialvcs uf cacli Station imiepcndcol lv approadi ihc beam from above and bclow.In thc Operation position thc irppcr and Iowcr halves p i i r t i ; i l l y n \ c r l ap . Each dclcclur ] i l anc
•). Tlit- ZI-AIS nlUI'.HA
__L
pheatn
elp beam magnets
Z (m)
BU Vertical Dipole BT Horizontal Correclion Dipole BH Horizontal DipoleQR Quadrupoles QS Half Quadmpole BS Seplum Magnel
Figure 2 G: Tnp vicw ctf tlir outgoing proton bcam t ine logether wit l t ihr magnctic clenicntsof tlir H E R A proton beam linc. The positions üf tlic LPS stations Sl througli SG arc alsoshown.
has an clliptical cutout wliich follows tlic profilc of Ulf 10 o onvolope of the beam.
Togethör w i t t i thrcc HERA main dipole magnots (vcrt ical bonding) locatod bctwccn S<land S.3 ihr Station S4, S5 and SG form a spectromcter (figiirc 2.G). The insorlion of thcdctectors into llir- operating positions typicalty i.s startcd snon aflor tlic heams arc bronghtinto collision. Since tlu- insrrtion proccdwrc took aboiit fifty minntes and since tlic bcamconditions did not always allow safe insertion of tlir detoclors, only a rcdnccd integralen!himinosity is availablc for analyscs nsing tlic LPS in 199-1. Tlir officiency of thr dctrctorplanes it i 199-1 afler exduding noisy and mal fnnc t ion ing channcls (< 2%) was botter tlian99 8%.
Tracks are rrcniistruclcd in stagrs, proccoding from i n r l i v i d n a l h i t s to fiill tratks. First clits-trrs of adjacent l i i t slrips arc scardicd for in catrh delrctor plane. Dy tornhining pairs ofclustors bflonging to dilfcrcnt projections, candidatc local trat'k scgtncnts arc found indc-pcndfiitly in cacli drlcctor asscrnbly. All hits liclonging to a catididatc arc uscd to find thc-transvcrsc eoordinatc of thc track at tlic valnr of ?. corrrsponding to thc center of tho Sta-t ion. Tlir spatiaJ resolution of thcse roordinatcs is about 3tl (im. Coordinatos rcconstructcdin pairs of l i i lferenl slations arc combinod into track candidatcs and thc track monientnmis dcterniincd nsing tlio avorago rp intcraction vcrtrx. Linear matr ix ^itations rolato thohorizontal and vcrtical roordinatcs and slopcs of the track at räch Station to thc positionand stopp of Ihe tnick <»t thc intcraction vcrtcx. Thc mat r ix clcmcnts arc known functionsof r/,, the fraction of tlic incoming beam inomcnturti tarricd by tho oulgoing proton. Thcfunct ions doscrrhc thr l»oam optics including tho cffects of qnadrupolos and drift longths.The t wo eqnations fnr tho horizontal and vcrtical coordinates aro indcpctidcnt apart fromI h r cotiitnon dcpendcnrc oti r;, and can bc usod to ob l n in two indcpcndcnt oslimatcs of .T;,.If t l i e two valiirs ubtnincd arc compaliblc, thc pnir of coordinatt-s is rctainod äs a candidatc[wo Station track.
As ;i final stcp of thc pattcrn rocngnition, tlir«1 Station (nick randirlatcs are searched for»sing pairs of (wo Sta t ion e.an did a tos. If the two track ranclidates givc compatible niomcnta,
2.2. ZKUS Dctccloi
if tho projoction of tlie two Iracks 011 Nie hon/unlal plane coincidc ;md if l l i ry nse thesaino hits in thc conimon st i i t ion, the two candidatcs are mrrgod in a threo-stat ion trackcandidato. Two-station aiul thrce-staticm candidiitcs aro Ihon p;issod to n <'onvcn(ional inickHt t ing stago. A v' is minimi/ed w i t l i rospoct lo Hve track pi i iatnoters (the positions andslopos a( tho vortox and .T,,) and tho best track parameters. togothrr wi th the orror ma t r ixaro dotermincd.
Thc idignnicnt of tho LPS rclies on snr\ey iiiforination for locating tho detector planes alongthe boam trajectory and on high onergy proton t rncks for tocaling in tho horizontal andvcrtical diroction. Tho indiv i<l i ia l dctoclnr planos aro first alignrd w i l h i n onc Stat ion, (honthc relative, a l ignmcnt of tho slations isdoteniiined, and rinal ly tho throe stations are alignedrelative to thc ZEUS detoctor. Typical accnraeicK in thc hori /ontal an r l vcrlical clireetion arebottcr than 2(1 /im Thc actual path o f t h e proton beam is also delorminod. AM tho steps ofthc alignmcnt prooedurc arc doscribcrl in dotail in | I M ) .
Tho LPS in it 's 1991 sctnp accepts scattcred prolons in t l i e ränge .r/, > 0.1 anr l w i t h0 & fVP $> l GcV, wlioro Pjp is (ho transvcrKo inomoi i lu iTi nf the proton w i t h rrspoct to Iheincoming beam flircction. Willi thc coiif igi irat ion instaUcd in 1991 tl ir resutnlion in .r, isbottcr than 0-4% at 820 GcV and the P,,, rcsolulion is ahont ö Mo\'. Thc la t l r r is loss thantho intriusio transverse n io ine r i l i im spreiul in the proton beam al t l i c in len i r lmt i point (withrms of altout 40 McV hori/oiitally and abont 90 Mr\ v i - r t i ca l lv ) r l i i r - lo t ln - beam divcrgencoof s; 50 /irad in tho horizontal and =: 110 /irad in the vt-rtical plane
Proton Remnant Tagger PRT
The proton remnant lagger (PRT1) |.11| ronsists of two paiis of s r i n t i l l a t i o n (ounlers snr-roiincling the beam pipe po.sitioned at /=.j.lö m. l! i.s l i n i l r l mit nf twu laveis oT sr int i l lalorseparatod liy l min (hick tead and wrnppi'd in I ra r l (2 mm t h i c k ) ;m<l i ron (0..") mm t h i c k )shiclding foil. Each of the scint i l la tor lavors is split in two hahrs i i i r lcpendrnl lv read out l ivtwo photomultiplior tubes. The grometrical layoiit of tlii- PUT s i - i n t i l l a t i o n n tnnlers and thereadout channe) assignment an1 shown in Hgnro 2.7. Two coiintcis on <mc side of Ihe beampipo form a pa i raml covor l h < > same aroa. Chargcd paiticles (;m bc idenli l i i-d in M i r - PRT bya coincidcnce of.signals in the two connters of one pa i t . The PRT has an activo area 30x2Gcm2 with a hole of 6.0x4.5 cm* al the conter to arronumidatc l l ic ( I R R A boam pipe. Thegoometric auceptanco of the PRT extcnds ovor Ihe psendo-rapiilitv (i; - -In tim(?/2) rängeof 4.3 < r) < 5.8-
The PRTwasopera t ional for the first t i m e i n 1991. It t o o k d a t a w i t h a piopci vollage settingonly for part of the Imninosity ränge nsod in this analysis Thc (»vc>ral l tagging olh'oioncy fora coincidencc signal, of al loast l MtP in each counter of otir pair, for Ihr IM-I data lakingporiod i s87±3% |11|.
Veto Wall
The vcto wall (VW) is localod at thc exit of tho beam pipe t n t i n e l at *=-7.27 m It consislsof an 87 cm thick iron wall wi th ovcrall ilimcnsiotis of ö x G m' wliich is sandwidn-d by twolayors of strintülator The VW shields the main drlivtm against prodncis of Mir interaetionof bcani protons w i t h the rest gas (proton bcamgas i t i te rac l ion) cntei ing ih r - in torac l ionregion. Partieies whieh arc not comiiletoly absorbed can be iden l i l i f -d by Ihe l i n i i n g infor-
(12)Pb{1 mm)
(14)
13
Fignrc 2.7: Layout of ihr PHT1 scintil lation countcrs and thc rcadout channcl assignmcnt.
mation from signals in tlie Lau laycrs of scintillator.
C5 Monitor
Thc C'j brani monitor is ;i small assnnbly of s r i n t i l l a tn r s separated by Icad shccts posilioncdorthogonal to the hcam pipc. T wo pairs of small scintillators (ronghly 10x5 cm? of artivcarra) are ins ta l led abovr and bclow (hc brani pipc behind the RCAL at z=-3.J5 m. TlicC"> moiiitor allows lo dclt'd proton boamgas backgronnd occurring botwccn thc VW and Cöiising the t in i ing inforniat ioi i of tbp scintillators. Tu rc-jrct noisc and vcry Iow encrgrtic parti-tlcs, Signals arc accrpted only Sf tlicy occnr in tlit; scintillators 011 botli sidcs of thc Icad shrcl.
Small Angle Rear Track mg Detector SRTD
Tlic SRTD consists of tw« planes of l cm widc and 0.5 ein thirk scintillator st.rijis which arcattaclicd to tlic f ront of llic RCAL {/--1.50 in) . These planes arc arrangcd in orthogonaldirct-tions and rovcr a rcgion of G8xfi8 cni! around tlic licam pipe. Thc SRTD scrves äs aprrsainj)l<T for scattcrcd clcctrpns in ordcr to corrcct for cncrgy loss. Thc tiniing Informationis userl to discri ininatc proton bcamgas inlcractions dose to llic intcraction point.
Thc VW, C5 and SRTD dctoctors discriniinatc bctwccn parttclcs coming from a genuine cpcollision al l l ic nominal intcraction point and from upstrcam proton bcamgas intcraction byprccisc incasurcniciil of thc titnc of thc hits in thc scintillators relative to t!ir. bunch crossingliinc. Particlrs froin proton bcamgas backgroiind occur at timcs 2j;|/r befure ihr arrival ofparlirlrs from rp tntcractions at ihr ZEUS intcrartkin point. Tlic carly timing is thcrcforc actcar indicalion of ( l ip proton Ix-amgas barkgroiind. In rase of a signal cnnsistcnt with pro-ton liramgas t in i ing thcsc dot.ctitors send a vcto signal to tlic global first Icvcl triggcr (GFLT).
2.2.4 Trigger and Data Acquisitiotl System
Thc n-iinirnncnts on l l ic ZEl'S triggcr anil rcaduiil s\stdii ;nc givt-n b> l l i c I IF .RA bunclicrossing intcrval of 9G ns and Ihr total nii i i ibrr of 2-")()()()() ZEl'S rradont rhanncls . ThcZEl'S data aapiisilion and triggrr systfin lias tu vcducc Ihr i aw inpnl d;ita slrcain of 5TRiIcs/s lo iiboiit l MDytcs/s \ \ i thoi i t rcjccling ton iiiany i i n p n i l a n l (ihvsirs rvrnls. TlicSystem consists of thr rcadonl Systems o f t he ind iv idna l coTiiponcnls n t n l a t h t cc li'\cl triggcrSystem, äs shown in Hgurc 2.8.
I I F R A : zr.llS:n n riurnh Z5o oooCnmJne Inlrrml Rodmil (.InnnHi
C-np .1
JL_ ._
D.i.
rD.I.
R«fT«
•
CompcM1 Swbttih
_L
n,T
-*.
Sl.T
«ntT«l
L-
> i l l /» \ l i1 i t r r
|GFLT|
ir
\ ; /1 1 * F t
t
. \ \ / /Ercnlhiiildlr
1 1 1 11 ThlrdUvtl Trigger
l-«r«ni „
1IjWllI
H T
-'
sl.T
ConSubi
*--
npo)n*M
_L
DK.Plprllnr
-pl
n,n,w
xnl•m n 1
_^^
1 t]
Figurc 2.8: Layout of ihe ZEUS triggr-r and data iic<|t i isi l , inn svstrm (I roui J79|) Nnmbcrsarc dcsign valucs.
2. '!'!,'• Z/i l'S ').'(.rim at l Ml t A
Earh ZEUS dclci-tor cunipoiH>nt is cc]iiippcd witli ils own fronl-cnd elcclrnnics Once adclector conipinK'iil lins bccti rcüd out, thcdal a isstorod in a H).«l M H/ pipcline find analy/edby n local litst levcl triggcr witliin the ticxt 2ö cltick oyclcs. Tlic rrsiilts from the diffrrcntcomponcnts rrfcrring lo Mie samc boani crossing arc input to thc global first Icvcl triggor(GFLT). Tlic GFLT calculation takcs additional 21) tninch crossing (1.9 ;<s) and ihr ovcrnlldecision is isstied cxaclly 4G crossing (4.4 /is) aflor the bimch that produced it. Tlic GFLTdccisioii is send luick to tlic componcrits. Thc inaxinmm rate of GFLT acccpt decisions isdcsigned to bc l kHz. L'p to this stagc bot h tlie triggrr and rradont arc dcadtiino frcc.
()n GFLT arccpl, dala accrplr<I for fnrthcr analysis arc copicd to a secotid lovcl triggcrwliicli is still local to tlicr singlc- i-tmiponciit .suksystcin. A GFLT accqil rate of l kH/. and acopy tinir of 30 /ts froni tlic FLT to tlic SLT pipclinc rcsults in 3% dcadtinic. A local scc-ondIrvcl triggcr conipntrs tlir triggrr Information whicli is forwardcd to tlic global scconrl Icvt'ltriggor (GSLT). T)ic GSLT conipntrs llic global sccnnd Icvcl triggcr dcdsion whicli is sendback to tlie coniponcnts, Tlip GSLT is drsignrd to vcto approxiinatcly 90% of all GFLTtriggcrs.Tlic coniponcnt data acccptcd by tlic GSLT is givcn a GSLT dccision nunibrr and trans-fcrrcd to thc Evcntbniltlcr. Tlic Evciilbnildcr cnrnbinrs aml fontiats all tlic cotiiponcnl datacarrying llic samt1 GSLT dccision nnnilicr into onc data sct, thc so callcd cvcnl
Onrc an cvcn! is complctc it is liandcd mrr to ihr tliird Icvcl triggrr (TLT). Thc TLT isa proccssor farin consisling of six branchcs of a total of 3G Workstations. A singlc cvciit isanalyml by an individual Workstation Bascd 011 tlic rcsults a final filtcring is donc and thcdata is writtfii to magnctic tapc at a TLT oulptit rate of aboiit ü rvcnls/s for rrronstrnctionand offline analvsis.
Reconstruction and Offline Analysis
F.vcnts froni tlic dctcctor arc rrconstruclcd by tlic program ZEPHYR. Thccalibration of rächdctcctor comnonciit is availablc and Ihr raw data outpnt äs \vriltcn to tapc is convcrtcd intor|iiantitics nscful for thc physics analysis.
A subsct of physical valncs in a rcditccd data structurr, llic so c;dlcd MiniDST, is storcdon 600 GDytc of fast liard disks conncctcd to a SGI Oliallnigc DM niachinc acting äsnn I/O scrvcr to t ho farni of hard disks. The data is casily acccssiltlc froni thc analysisprograms ninning on two SGI Cliallcngc XL mnltiproccssor marhincs. This System is accntral coniputing facility of thc ZEUS cxpcnnictit, tlie so callcd ZARAH.
Chapter 3
Photoproduction at High Energies
In tliis cliaptcr tlic kincinatir variables uscd tu dcscribc r/i inirraclifuis arc lirst introduccd.It will bc cxplaincd how rp intcractions can bc nsetl to mrasnrc plintoprodnclion (",}>) crussscctions. As thcn disciisscd, ccrtain, photoprudnctinn ini.crfirtiotis i-an bc describcd in thcfraincwork of t ho vcctor mcson doniinancc niodcl (\'DM) and ftrggo pliciioiiieiidlogy. Thedcscription iitclndcs thc cruss sottimis and dccay anglcs
3.1 ep Interactions
A (liagrain dcscribing the scallcring of clcriwns off prohms in first nrdn ctcrtroinaguotkpertiirbation theory is shown in lignrc 3.1. Tli'1 fonr ninnicnta of (hc partiolos ;ire gi\'i*n inbrackcts. Tho kincniatics of an r/i intciaction can bc dcsfribcd by llic r;» n-ntcr of inasscncrgy )/s ts J^F,fEp, ivhor«1 /T, and Ep arc ihr cncrgy of Mio innxning clcdron and protonrcspectivi'ly, and any pair of tlic fnlluwing variiil'lcs;
? = _q ' = _ ( k _ k < ) 'v - FV = r-
niininial (3.1)
(.3.2)
(3.3)
2qp
For
(3,1)
(3.5)
In llic electroueak theory the oxrlinngrd gange boson in a iifiilrat ciurnil inlcia<-tion ntavbc a photon (•>) or a neutral wcak \celor boson (Zn). In l.hc kinnnalic ränge of inlcrcst inthis Ihcsiß (Q7 < AGcV2) Z° cxcli;ingc can bc safcly ignorcd.
The clcctrornagnctic inlcrnction bctwecn clc<-trons and prolons is givcn by [M]:
(3-0)
wlicrc r> is the elcctroniagncüc conpling i-onstnnt \\hile E Jind E' arc thc cncrgics of tlicinconiing and oittgoing clcolron in tlic pmlnn rosl frarnc rospcctivi-tv, /,"" is t In- loptim
fjnii al llixlt
Figuro 3.1: Sclicmatic diagrani of rp scattrritig in lowest ordcr in o.
tctisor:
L"" = 1 k'" k" + k* k» + —V1'
and U',,,, tlic liiidronic (nisor:
(3.7)
(38)
iinH Mj arc t wo inck'pcndciit incl;istic stnicturc fiinctions. Altcrnativcly thc hadronicciin lic writ tcn äs
(3-9)
wlicrc Ihr Rinn nins ovcr all final statrs | A" > and spins of tlic inconiing ptuton | p > and jt,drncilps thc Hoclroniagnctic rurrmt. Thc clifft'rciitia! cross scction .1.6 ran also bc cxprrssedin [crrns nf v and Q7. Evaluating L''"\\'I1V using cqiiaüons (3.7) and (3.8) tlic dilfcrcntialcruss scrlion rcncl-s:
(3.10)Q2
3.2 Relating ep and 7^ Cross Sections
In llic folirnving wr rcst ritt oursclvcs to tlic prcituii rcst franic, so tlic photon fonr inoincntuntis givcti tiy q - (", K). In this Trainc llic total cross srrtitni for stattcring of real pliotons ofcncrgy A and polari/.ation f j "ff nnpolari/cd protuns tan bc obtaincd frnni Fcyninan rulcsto lir:
(3.1l)
;).,'<. 1'lnttt»i-/'t"tun l l r lr iart iuiis 19
Tlic diMcrcnti;il cross scction for itidastk c}> scatlcring (3 (i) citn bc iiilcipiclcd äs ;i virtiialplioton pioton noss scclion o"1 ". Ruf. CHIC has to kccp in niind tliat real pholons c;m orcnrin tw« transvcrsc polamatioiiR, whcrcas virtiial photons can also otrur in a longitndinalpolari/ation statt, tlcal photons havc a flnx factor \Mr!\. For vir1n.nl photons tlic flnx is
nol iinifiucly <lcfincd. Tlic totivcntional appioach dnc to Hand |."»5] reqiiircs tlir iiionicntiiinA" of Ihc virtual plioton to bc cqual to tlic rncrgy of a real ptiolini ncrilcd !o givc thc sanir
"*:
KH,n,< = n'v^~ Q (3.12)
wlicrc i' is thc cncrg,v of thc virtiial plu<!on. Dvlining thc / axis along thc \irlu;)l photonmonicntuni A', thc polamation vn'tor f'^ is givcti by:
A -
(3.M)
Using tlie (Icfitiitinn of !!',,„ (3 8) logctlicr \villi t In1 almvc potari/atinii virtitr nur finds tlictransviTsc and longitndinal rross siu-liun In bc:
(3.15)
(3.1G)
Für •)']> scattcring iit sniall (}*, Bjuikcn r is sitiall and nw can appioxinialc A" Ä; i/ andl + iS/Q7 K v*(t?. Tliis yiclds:
(3.17)
(3.18}
Nrglccting tlic tcrni iU'/s in cqnatkm (3.10) iind nsiiiR llic ri'latinn (Jf,,,,, = A//i/'/(l - y)yirlcls thc following dilfcrcntial rji cross scclinn
3.3 Photon-Proton Interactions
In thc prcvious scction il was sliowii that a t-p cross scclinn nicasnrcd at MRRA can bc
rclatcd to a virtlial photon protoll rross scrlinn. In tliis scctinn ;i llicoir-tical tnodd nscd to
dcscribc 77? intcracttntis will bc itiLrodnccd.
3.3.1 Vectur Meson Dnniinance Model
Plinhm hiidrnn intcraclions ;it liigh cncrgics cxliiliil siimlar properlics äs hadron liinlnm
iiitcractions. ()n a f|iialitiiti\ Icvcl tliis sitnUarily can bc nnderstood äs fnllows. Tlic unccr-tainty principlc nllnws Miictnntinns of Mir pholon intn ;\l i/ij statt1 of (In- samt? qnanlnm
iiiiinlirrs äs tlic pliolon (,/''c - l"*; Q=S=D=()) namcly vector mesons. In ttiis snlecclionwc rcstricl uursi'lvcs again to t In* proton rcst n-fiinc so Mit- plinton fonr morncntuni is givcn
liy t] - (c, A"). Tlu1 fliictualion liine is givcn by
''" <"•»If tlip dislancc1 (hat thc virtual vcclor nirson can travcl is rmidi largcr than tlic nucleonrailius r i, ~ l fni tlic plioton fluctuatcs lorig bpforc. it hits thc liadron and thc inloractionoccnrs bclwccit thc vector mcson and thc hadron.
Tims thc pliysical photon \ > can bc considcTcd äs a superposition oF a bare photon | 7« >and a liadronic componcnt ^/ä \ >
|7 >= \fZ3\lH > + «yo | / ' > (3.21)
wherc Zj assnrcs thc proper nonnalization. Although thc liadronic plioton coinponcnl issnjiprcsscd by v/a, it dominates Iow (V2 plioton proton intcractions sincc hadronic crossscction are vcry largc. Pholoproduction oF thc lichtest vector nicsons p°, u and 0 snggcstsihn t thcy providc a vcry imporlant conlribution to | h >. Only considcring these. vector
tnesons äs thc liadronic coniponenl and neglecting thc bare photon | "JR > contribution isthc hypotliesis of thc verlor dominanci1 tnodcl (VOM). Thc inclusion of morc constitncnts to[ h > is rcfcrrcd to äs gencralizcd vcctor doininancc inodcl (G\'D). Rcviews of thcsc modcls
arc givcn in |10| and |32|.
For Ihe VDM thc liadronic photon componcnt can bc writtcn äs:
r=p".ii.j.* * c J
whcrc /(• is tlic •> «-+ l" couplJng Thc niatrix elcmcnt for pliotoprodnction (7/1 —» .V)< X \ \ > can thcrcForc bc rclatcd to tlip niatrix cleinent Für vcctor mcson photonscaücring (Vp -t ,Y) < ,V | jv | p > by
wbcrc j dciiotcs thc eleclromagnctic cnrrcnt and jl thc currcnt of thc vpctor inoson ficld.Tlic cnrrcnts j (jl ) can bc scparatcd in a transvcrsc and longitudinal contributioti, in whichllic nirrcnts arp parallel j$ (jl ) or pcrpendicular j± (j[ ) to thc thrce tnonicntuni of thc
virlual photon (vcttor ntcson) A'. Thns thc virtnal photon cross scction can IJP calculatodiiccording to (3.11) in thc Hand convcnlion
Ä.spin
(32-1)
2nfV' v- i v , • i ,--J L. I < A \Jt\P >\l
Tlic icdoi mcson piolon cross scclion (\'p) is Jicfunlingly gi\cn In
IP - !L V V f ' l \ '' A' . ' ! -hM,,
(.125)
°).p = i:-1-^- E l<-V| j | !A",\..pirr
4t M.
Assnming tbat S.v.,P,n l< X l .f||.j l /' >l? l/t^'^pJ'^^?' - P - q) ^»rii's vcry liltlc wilh
QJ thr cross scctions (3.24) and (3.25) can bc rdatcd »sing i'f]iiation (3.23). This yiclds thcfollowing Q2 dcpcndi'iicc of aj " and o]: '':
. n / A / 2 \ ,ff?• (»V^ J = E -rr\ ... ^I'(»"i,,) (3.2ß)' ' 'r * ' i*-* II \ i / JJ l ' v ' V' ' /
, JTTO= ^ ~rr
-i/?TiT^ '(»•.,) (,127)
\vherp £* = (7,//o7•" is tlie ratio oF tlie longitndinal to trans\eise \'j> cinss scction [9lJ.
SincP vcctor nicsons arc sliort livcd particlcs i l is impossiblc to slmly \']> scadering di reell v.The additive quark inodcl [68, C9. T()| 011 thc otlicr han>l alluivs to rclalc l'/jcrnss scctions tu
iip and A'p cruss scctions, since in Ibis nmdrl llic intcraclinn bchvccn hadrons is dclcriiiinc.«!by thcir vaJcnce qnark constitncnls. Tliis yiclds thc FuMmving rclations:
^f^ofr K ^ (^" ' " - t ff* '') (3.28)
a*" « rtht'' + r T h " " - ^ " " p (3.29)
Photoproduction proccsscs arc classilicd similar lo dadron hadron inlcractiotis. AI, highcncrgics cvents with jet likc strnctnrc, callcd haid iilinloprodnrliiin, arc nliscrvcd. Thc
cross scction for lliis process is MTV smull and haul plidloprinliirtioit PS not iniportant inthc present analysis. Thc bnlk of liadronic. inleractions is charactcrizcd by Jow transveise
nionienta and traditionatly rcFcrrcd to äs soFt processcs S<iFt liadronic proccsscs can bcdcscribcd pbcnonicnologically hy Ficgge theory (scction 3 3.2). Tbc Following classilicationis conimonly uscd for soft photoprodnctinn.
• dilfractive pliotoprodiictiunTlic nanic oF tliis evcnl cla.ss originatcs Fmni analoges to tln1 difFraction oF light by acircular apcrture [48]. DilFractive pliotopro'lnction is classificd äs follows:
rliffraction (7/7 -+ \'j>, V" : /»n,u;, 0)
In VDM this prorcss i-s thc analog to thc clastic sraltcring prnccss in hadronhadrnn collisioiis. Thc relative coiitribiilion fif claMic dilfiaclion tn thc total
pliotoprodtirtion cross scction is similar to thc rclalivc conlribiilion of clasticscattcring in hadron litulrni) collisioiis. Elaslic plinloprtidiictinn >,( />" incwmsacconnls for ~ 8(1 % of llic claslic dilFiactivc r MISS scf lion and is llic inlcrartionstudied in Iltis thi-sis.
.1 l'/ioN'/innfnrf.ii'll .1l
- d i f F r a e l i v e dissodationIn l l i i s cvetit class at leasl one "f thc inconi ing parliclcs dissodiilcs into a highermass statt1 (Af or ,V wi t l i .l/\ M\ M.\ /U,,). DifFractivc dissoriative cventsarc classihcd äs folloivs:
t proton dissociiition (tp —> \ ' N )
• pholon dissociation (->p -t ,V/))
* double dissociation (~yp -* ,VA')
Thc cross section of thcse proccsses has bccn found to approximatcly fultuw at agivcn MV
-« ,. !* ,t (3.30)
witli n = l [48]. The slopc paramctcr b dcpcnds on thc mass of the dissociativrSystem A/"iv(x)- For singlc dissociation and masscs atmvr tlic rcsonancc rcgion, 6is ruughly half Uie valuc for rlastic Fral tcr ing.
nun dilFractive pliotoproductionTlic rnnaining cvcnts arc callcd non-diffract ivo. Tlicy arc nsuiilly descriln-d by phc-notncnological modcls.
3.3.2 Regge Phenomenology
Tiic high cnrrg)' bcliavior of hadrotiic cioss soctions can prrsrntly not bo dptcrniincd fromQCD, ttir microscopic thcory of t ho strong in tc rac t iun . Phcnonicnological modcls basodon Rrggr's idca of srattcring aniplitudcs analyt iral ly cnntiinicd in thr coniplcx monicntnmplane arc a possihlc approach to this da ta (23, 24, IG] Thosc propcrtios of Hrggc thcorywliidi arc of mlcrest for tlic analysis prcscntcd in lliis tlicsis arc shortly simimarizcd HCTC.
Tlic strong intcraction bctwrcn hadrun.s involvc tlic cxc hange of quarks and glimns \vithoutnct color t-xdiangc, t l ius objrcts likc mc.suns and baryotis arc cxcliangcd bctwccn stronglyintcracting hadrons
n egge tlicory makcs nsc of Ihr so callcd crossing syitHiiutry shown in figuro 3.2. For thcpmcpss ,40 -4 CD s is thp squarc of thc ccntcr of mass cncrgy and ( thc squarcd four-nui tncntuni transfcr. ( is rclated to thc scattcring angle 6. In thc crosscd channcl AC —t BDthc niergy is givcn hy ( and tho scaltcring angle rclated to s. Sincc thc quant imi numbcrsof thc cxcliangcd tibjcrt in thc s-clinnncl rcaction (Aß -t CD) and thc t-channcl rcaction(AC -» ÖD) are thc sanic, both processrs art1 assuincd to bc dcscribcd by a coinmonsrattcring aniplil i idc, bat in diffcrcnt rcgions of tlic variables s and (. Thc anipüliidc A ( s . t )can be pxprcsscd in thc f-channcl partial wavc sciics by
(3.31)
whcre P( arc the Lcgcndre polynoniialsand .4,(f) l he /" ' -purtial wavc ampliIndes Thc parl ialwavc amplitndc can bc idcntificd with a piopagatnr-l ikc Icrin for llie c.irtianqrtl particlcs
Figtire 3.2: Dtagrams of ihc .«-channcl (,-lß -* CD) and f-cliannrl (AC -t /)D) jtroi'i'sscs\vliich arc rclatcd by crossitig symmctry.
wlierc F,(r) is thc partial dccay wid t l i of a givcn particlc of mass n i j . Now Ihc scalt i-r ingamplitndc wil l bc continncd ti)coniplcx angular nioincntiitn l. This cnablcs tu n r i t c ihc stmi(3 31) äs a Canchy integral:
paii,(.1.33)
Stndyitig thc (-channcl rpaclion, it WMS expcrinicntatly fonnd t l i a t t In- n-simann-s whirh ranbc exchangcd for a particular choicc of thc colliding parlidrs lay on a slraight l inc in ihcChcw-Fraulschi plot (spin .7 versus mass » t 7 ) . This nliscrvalinn snggrsts, tha l fur a givcnisospin and strangeness a fnnclion / = O(T»'), rc lat ing tn;iss and angnla r inn inr i i lun i , cxisls.Expanding this function in a l inear fnnction (<t(t) - r t ( U ) + o'/) arouiul inj - / :
This can bc nscd in c(|uation (3 33)
.4(- , / ) = 5-/ .«£1 Jptttn 2 s i l l 7 T /
(3.31)
(3.3.-.)
Instcad of an integral ovcr ii iany polcs in rquntion (333), thc a m p l i t n r l c is no\ given by anintcgration aronnd just onc pole / = c > ( f ) in Ihc complex f plane
Assuming that thc integral v;inishes on a propcrly chosen palh the i n t c u i a l rnlurcs to thcrcsiduc of thc pole al o(() = /:
r1"' ± l (3.30)' - V - ' - / • • „ • 1 ^ ^ ' ' / ' O l l l l, ' ' T I I M ''2s\nxl dl
Thc funct io i i ( t ( ( ) - n(0) + (t'( is nsiially calleil Ihc Reggc trajcctory, represrnt i r iR a wholeseric-s of exchangcrl resonanccs of givr-n isnspin, slriingi'tH'ss and par i lv
Thc asvniptotic bchavior of thc i impli lnclc for thc reaetion AR -t CD, in u-hii h / is negative-and \l\£ -s ran nuw I M - wr i t t t -n äs
(3.37)
Nchannelregion
Figiirc 3..l The valnes oF n(f) (For ( < 0) obtained by fitting td TT p -» n°n data logolhor
witli ihc extrapolatinn üf tliu linear p trajrclory (From [24]).
sinee for ( r j < s : /'„(ijfiw^) ~ r"""1" (.s/.s0)""'. The differenlial cross section in tlie [wo
botly procoss is therrFore predictrd to lie:
(3.38)
The trajectory ct(f) can bo dcterminrd by plotting \ndo/dt äs a function of Ins at fixodt Fignro 3.3 shows thc nicasurcd p trajectoiy for thr ,e-channol rcaction fl~p -> TTOH. Thn
points line up nicely with the rtwnanccs belonging to thc p-lrajoctoiy (f-channel reaction
7I-7T0 ->fln).
The optical theorem rrlatcs thc total cross section n'"1 to thc imaginary pari of the forwardelaMic scattering ainplitudc (o'ül - l/s!3(/l)|,^o), so thc forward düfcrcntial cross section
can be writtcn äs:
^ = 7^0+'/W°')2 (3.39)dt t=0 l Off
wiiere fj is the ratio of the foiwanl rc.al pari to the forward imaginary pari of the scalteringaniplitiide. Thc optical thcoreni togclhcr ivilh rquation (3 37) leads to:
n""<x ,»('=")-'. (3.40)
So the high energy l>ohavior uf total hadron cross sections ts detcrinined hy ihc highest lyingtrajectories, which in the Chcw-Ftautschi plot are the dogencrated w// and p/a! trajrctorios(f VwC — 0) 5= 0.5) They wonld lead to a total cnvss section n'"1 oc s~ l /z. This bchavioris not observed in hadron proton iiiteractions at high energics. Inslcad total cross sections
abovc v/S = M' RS 10 Ge\ are slowlv rJsing. This implies. thal if a RCRKC poh1 exchange isthe dominant mochaiiism, there lias to bo a Irajeclory, callcil Ponieron IP with 'i|>(0) > 1.
Il is genorally snpposcd tliat the Poinerot) rcprcseiits gluon exchange [30, G7|.
Tito sloivlv risingcross .section can he exjitained hy ftp.(O) > l, however such a power hehavior
shonld not continno iiidorinitcly duc to pnrliaf wavc nnitariiy. Tlie total cross seclion has to
fnlfill tho Froissart-Martin hound:
o'°l < -^(lu*)'- (3.41)X
It rs cxpected that the simiiltaneons exchange of inaiiy Ponicnms will cliange the asymptuticbchavior (CT'°' oc s"»-!0)-1) |O at nu»st a (In.s)2 bchavior.
Total hadron proton cross sections can ho snm-ssfirlly lille«! hy a sinn oF tivo tcnns, oiie
duc to thc exchange of tho highest lying fleggeon trnjectory (/>/".2i"V/) Mtl(l (1|K' '''"' '" '''(•'Porncron trajectory. Such an ansatz lias the Form:
o"" = A'.s' + r.s-'" (3.42)
where i; and ( are effoctive exponents For Reggeon and Ponieron oxrhjtiige. They are assnniedto be thesanio For difforonl intoracling haibntis, while .V and V fiepend im the proccss nnderstndy. Donnachie and Landsholf [36] nsetl />;» and )>f> dala wilh v/s > III G{>\ and found:
( - 0.08118 i] = 0.4:.2:> (3 43)
They nsed theso powers also to fit the valncs for A' and T for variotis cither liadion pmloncross scctions liko ^*p, K*p and 7/1 Recently CJirdell et al. [20] icpcaM-d llie lils of F)fin-nachic and Landshoff to /»;i and jtft dala. l'sing (illcrcd d;tta and non degeneraled Rcggeoiitrajectories (nlot = \s' -t- )'_.i~" 4- l^s"1'*) their best estiinate Fnr ihe Pnmenm itileicept
((>i'((J) = 1 — f) is f = 0 096*fj009 ''"' se\'eral modi'Is hav'e a goorl \ For \"itnes of t in llieränge [0.07,0.11]. In a very similar npprnach Cmolan ei al. (25] pcrforined global lits tototal cross seclion and ij valne dala for j t ^ j i , n*p and h'*jt with ^/S > (» Cie\'. They ohlained
tlie swondarv Reggeon trajectorios frorn fits to thc //« and «.•//> rhew-Frantschi plot andfixed tho slopo of the Ponieron trajecliiry (n^, = U.20 (;e\'~J). A Rom levol simiillaiii'ons
fit lo tho data yields a Pomcron intorcept of (i|-{!)} - 1.104 i 0.002 antl using an eikonali/edamplitndc thcy obtain nr(0) = l. 122 ± 0.002.
Tho exponents ( and tj are efFective exponents, nheie jj acconnls fnt fonr indepmdcnt tia-
jectories and a Iower onorgy cnt lias to bo introdnced to exclnde lowcr Irajectories. Theoxponenl r is cxpechsl to show a (slow) tlcpendetice on s to iis.snte llie Fmissarl-Mailinhonnd (3.41). For ^s > 10 GeV and tip to the liighest avaifable energ> (\ = 1.8 TeV atthe TEV'ATRON J40, 20]) the simple fit accordiiiR m er|iiation (3.-12) is very sncceshfnl.
In lindron hadron intoractions it was Fonnd that For valnes \t\ 0.3 CieV2 ihc elastic dilfer-cittial cross section da/dt falls roughly exponentiallv with |(|:
Theexponenttal hehavior suggests (hat //(() inof|nalion (3.38) can he wril icn a s y ^ f / ) - /Vwhich, assuming a linear Ponieron tra.ject.ory, loads to:
da / « \"p")-2
~di
*" thatfr = o + 2«'rln—. (3.4G)
*Q
Thiis Ihc fonv;ird pcak sharpcns äs In s incrc-iises. This eifert is callcd shrinkagc from whtchtlic slope of the Poincron trajcclory tan bc dclcnnincd. Elastic pp and pp scatlcring yicld a
of[33, 34];o',. =0.25 GcV2 (3.47)
3,3.3 Elastic p" Photoproduction Cross Section
Elast ic (t° pliotoprodnction can bo mcasurcd at HERA in thc rcaction
(3.48)
Tlic /)" mesoti dccays alinust exclnsivcly in a pair of chargrd pions. Tlic analysis prrscntcdin tliis tlicsi.s is rcstrirtcd to sinall valncs of Q*. Tlic upper l ini i t on Q* is Q^,az « 4 GcV*and t l i r nicdian QJ is aliunt l()~s GcV7. Only cvcnts in wlii<-h llic oiitgoing clrctron was notdctrrtcd in thc ZEUS drtector arc acccptcd in this analysis Tlir kincniatic varialilrs nscd todrsrtibc thc proccss arc the invar innt plioton proton ccntcr of mnss cncrgy \V-,P — J^E-,Ef
(or al trr i i i i t ivcly y sä E^/E,), whcrc £T is thc photon nicrgy and thc iimnicntnni transfcr atthc protun vcrtrx ( = (p - p')2, \vlicrc p anit p' arc thc four rnomcnla of tlic incoming andoiilgoing protun rcspectivcly.
For k inc tna t ica l rcasons a minimnm nioincntnin transfcr is ncccssary for thc transition 7 -4p°. So llic following condition has to bc full i l lcd:
g')'(3.49)
In llic k i n c n i a t i c ränge nndcr stndy !,„,„ is ofordcr 10 " GcV2 and tan bc safdy sct to zcroin llic following.
As cxplaincd in scttion 3.2 rp scaltpring can bc rclatcd KI t l i c scattcring of v i r t u a l photonscm piolnns (3.19). Thc VDM rclates clastic -jp to chislic l'p rruss sccliuns oy thc conpling
For clastic />" photoprodnction cqiialions (3 26) and (3 27) tlins rrait
(3.50)
(351)
(3.52)
Insrr t ing Ihcsc in cquation (3.19) yiclds
(3.53)
J.J. 1'lnilun- /'n)[(ii!_fntrracttti»s
(.1.51)
is thc. cffi'clivc plioton flux.
A mcasurcd p° clcctroprodnctiun noss scction (r;) -+ r/v1") '"<" 'hns be tratisfonncd intoan clastic p0 photoprodnction cross scction (-j;i -> pn]>) by divifling thc ck-ctKiprodiictioncross scction by thc cffcctivc [tlioton Hux intcgrnted over tl ic y and Q7 ränge covcrod by themcasnrcnicnt.
Applying thc optical ihcorem (3.39) to /j"p intcraclions yickls:
, = TG* +'')(fT""'1'
whcrc 1} has bccn mcnsnrcit a( high encrgies in hadron hadron inU- i i i c t ions lo bc of thc-'ordcr111% |G1] and is sei to U hcrc. Since VDM relatcs 70 (o ff p cross sections onc can wr i tc :
dt
Using thi1 cxponcntial bchavinr of clastic /)" photoprodiiclioii 'nie can wri lc tlic cross scttionäs:
l7rn * " > '
Thc additive qiiark modcl vrlatcs <r'"' lo weil mcasnrrd li;«lmtii<- noss .si-tliuiis liy:
(3.57!
(3.58)
Thc slopc b^-.uscd, assnining
has lo bc fixcd, too Again , nicjisnrcincnts of n + /» inhTar t i iws ronld IM-
t-.p-.p«,, - b»*,.~,.*P- (3-59)
Tliis approximation fit,s well to Uic data (K) , Gl |
The cncrgy bchavior of hadroii hadron cross scctions and cnrrgy hchavinr of thc slopepararnctcr b is describcd by Hcgge Micory ((3-12) and (3. I G ) ) . Using tlicsr rclations andcr|iiation (3.57) llic rlastic (P photoprodnrtion cross seelion ran bc prnlirh'd, if thc 7 (Pconpling /po is VIKHVII. Donnachic and Landsliolf [37j and Srhnln and Sjös t rand |97] nscdtliis proccxlnrc to picilict thc clastic (i" pholoprodiiclion crnss scction Thcir prcdicLiitus an-approximatcly ll)%-2(t% higher thari thc mcasurcd valiit-s. This can be cxplairicd l>y llicconpling cunstant /^o used by thcse antliors. Thc ronpling can bc delCTiiiincd iliici tly fromihc from r*r~ collisions sinco ihc c*c~ deray width nf thc ff* is rclat.cd lo thc conpling by
F(^° -» r*r-) = «2/3(/^/4H| , -) ' Mf- TI"' wi|'li"R /^/4» , is snuillcr llian thcconpling dctcrinincd from pholnprodiiction dnta /i/'ln |l(l] relevant in thc anidysis of claslic(P photoprodnction. Tlie dilfcrence in thc conpling oblaincd from rV~ lollisions and frninphot.')pro(lncti(in tnighl be canscd by in l r ins ic i incrTta in t ics in VDM ;unl liy thc modcl de-pendcncc of ihc detcnnii iat jon of thc photnprodnction rcsiilts (jissnming thc ;u ld i t i \ ( j n a t k
^ 403 35"a 30
20
15
10
5
0
VOM & Pomeron (Cudell et al.)VOM & Pomeron (DL)
o Iow energy dato* ZEUS 1993* Hl 1994
10
l - l l _.!._! 1 L
10(GeV)
Figurc .14: Measiircnicnts and predictions for l he -)p —v p°j> cn-ss soction versus It'7p (froni
model) [49], Td In1 entmisten t \vilhin pliotoprmluc-tiun the umpling /3i/47T was dcfcrminedfroni clastic p° photoprodnction cross seclion mcnsnremcnts with H'.,,, > 9 GeV liy invcrtingixiualion (3.57) (fa/4x = 2.C9 ± 0.27 l«]).Figmc 3.4 show.s prcdictions for tlu- clastic pn plioloprodnclion cross scction [49] togctlicrwith Iow eticrgy dnta tiscd to detcrmine fj,/4ir. Tlu1 full line sliows thc prodirtion usingtlii1 rc'sults of tlic paranu'lcrs givcii by Dnnnacliic antl LaiidshofF (3.43). The dashed liiicindicati'S ihc prt-diction for tlic rlastic p° photuprodiirtmn cross scclioii using a valuc for ( of0.096 äs dctcrtiiiticd by Cudcll t;t al. and die shadrd nroa sliows tlic cffrct on tlit1 prcdictcdcross scction by van'ing t bctwr-rn 0.07 and 11.11. Details on Ilic prucrdurc usrd to drrivc-tlic prcdicLions in figurc 3.4 arc givcn in [49].
3.3.4 Decay Angular Distribution
Tlic />° drcay pions can bc itscd äs an analvzcr of thc spin slatcs of tlie p°. Analyzing thr p°drcay disfribution nllows to study thc spin drpondcnt propi-rtics of thi' production procrss.Tlic relrviint fornialism lias bccn dcvclopcd in [96].
Tlic angnlar distritnition of thc decay pion is stndicd in tlio ^° rcst framc. In tliis framca rigbt handln! coordinatc systcm is drRni-d äs follows. Thc f - z plane is thc productionplane (Yp° planr in thc liadronic ccritcr of mass systrni) and j/tlir normal to tliis plane. Thc(jiiantixfUion axis ran bc1 thoscn in ditTcrcnt ways. A spccific clioicc is tlic s-channcl hclicitysystctn iti wliirli llic faxis is nppositc to tlic dirrt'tion of thc onlgoing protnn. Tliis framc istlic inosl ronvcniriit syslcm for (lese ri bin g tlic f>° drcay in plmtoproduclion |l()|. Thcnretiralaspccis nf s-rhatincl liclicity consrr\atioii in diffrarlivc scatlcring arc discusscd in [IG].Tlic polar nnglc 0h is dcfincd äs tlie angle br-hu-cn thc n+ and tlic f axis and tlic a/inmtlial
Lob System
Virtuol Pholoproductionc.m. System
Rest System of p*
Figurc 3 ö: Thc /i° decay anglcs in thc s-diamicl hcli< iiy sysirm.
angle $,, is thc angle betwecn the prodnctinn plane and ihc dccav plane ( T T ^ T T " plane in thcp° rcst franic). A third angle <t> dcnotes flie angle beUvrcn thc prudtirlinn ]ilanc and tlicelectron scattering plane. All thrcc anglcs arc slimvn in lignie 3.0.
Thc / dccay angnlar distribntion irfeos-9,,, 0,,, -t) will he slndicd in Icrms of thc ,»" spindcnsity matrix (%]. The p" spin dcnsity malrix /> in gcneral can bc dccmnposed intü nineindcpcndent niahiccs p", \vhcrc ihc nialriies n - I) in ,1 and 4 desi ribe p° prndnctionby transvcrse and ti-ngitndinal photons respcctivcly and ihr- nuitriccs o = ~> i.n 8 inrasnrcinlcrfcrcncc bctwcen Iransvcrse and Inngitudinal pholutis
In the analysis presentcd in tliis Ihrsis thc Inngitndinal and ininsvcrsc phnton llnx (T,., T/}cannot bc varied sr j ihc matriccs//1 and p' nimmt bcsepatalcd. The follr.wing cimibinalionstif rnalrix elciiicnts />',\c thcrefore incasnrcd:
i + S) n
.(. f '/n iliijiniilitclinii .'l / / ifi l i
n - l - 3
n = 5 - 8
/? =
l +2(1-
-5 =Q*
(3.G1)
(3.ß2)
(3.G3)
(3.G1)
(3.G5)
H is llic rntio of ihr cross scctkms Tor p° photoprodwlion hy longitndinal and traiisverscphotons. l'sually in p" cloclroprodnclion pxperimcnls Ä is nrglcctcd and QJ„„„/Q1 == 0 sof rnlnrrs l D f — (2(1 - v))/( l + (l - y)2). Fnr ihr atialysis prcscnlccl in iliis thesis thescapproximations are nut good sinco the whntc (V3 spectrum down to Q*„„ is nicasnrrd. TlicV dcpendciHT of f sind 6 in thc ränge undcr study (ö(J GeV < H'lp < ]()() GcV) is vrry smnll.Q7 is mit mrjisured in tliis analysis, so in thr fullowiiig ( atul 6 arc avcragcd ovcr Q* andgivi-n for thc tm-ait y:
(0 = 0.998
(t) = O.o:>2
£ - w + «The iiorinali/cd dctay angnlar distribmion of ihr
in Icitns of 15 spin density matrix Moments:
3
(3.GG)
(3.G7)
- l (15 (3.G8)
r* with an nnpotariml clrctron licani is
•Jl((\( +(i)sin*(v'2'-ir?0 sin
rf_,sin2Öhsin2* f t)] (3.G9)
tt-lu-rc TJ and '-i stand for the real and imnginary pari of llu- nmtrix cleinciit. If the clpclronsarr transvcrsely polar i/cd, thc fnllowing tcrms have to !«• addivt to cquatioii (3.G9):
cos a, cos1!' + sin n i sin <I> l (\r<?orf„sin 2W/,
cos n i sin "T1 - sinn( ros'T1 l (ru sin fl/, -f fon<'os f)h -
where o( is the angle Itelwmi thr plane of polarixation aiul tlie declnm sc;ilteriiiR plane andP is llic dcgrec of transverse polari/ation of the clcclnm lieam. M'lr >'"' conlaiiis a factorJnt/Q and llienTorc llie trnns in etjnation (.1.711) f,\\'f a si/i-ablc runtrihnlion tu the dccav
angnlfir distribulion onlv for Q <^ TU,. Fiirlhcrniori1 H ' contains a fnrtor l - <, For thcdatJi presented in this tlicsis Ihr avciagc i is (I.9DR and llicicforc (3.711) ran In- neglrrted. Soin thc folliming thc decay angidar dislrilmlion is giveti liv eo,nation (3.fi!)).
In llic casc ofs-dianncl hrlicity cctiiservalioti al the ">;> \'cilcx all spin densily matrix deinen t sexcepl T'QO, r j _ , , '-3r2_|, SJr',,, Virf0 , '-if'f0 and W>'*n an* /cro and F ' I _ , = — '3i'_|, Sr^o ~-l-ir*0, Ür[0 - ^rftn- Fiirtliertnore fnr s-clianncl hctirity rj| n>nsci\;ition l he followingrelation holds:
l r01ff^-^ 1«L_ ( 3 7 ! )
f + * ! - .« • ( '
Thcreforc liy nieasnring the cosflh dislrilmtion llic ralio ff ran he dcti-ntiini-il.
Sinee in ihr analysis presrnlcd licrc llic angle *!' is tinl ineiisiucd llie dera> angnlar disl.rilm-tion riflnces to:
HTt
(3.72)
Chapter 4
Event Selection
In tliis tliaptcr tlic Iriggcr and llic selirlion nits for claslic f>n photoprodnrlion cvciits willbr disnisscd. p° nicsons arc measnrcd in tl ic drcay diamirl /i° -t T T + T T " . Tlir Inandi ing rat.iois ~-iOU%. In tlic data prcscntcd, t l i c saittercd rltrtron f i n d proton cscapc rindclcclcd, soclastic p° photoprodiiction cvcnls arc cliaraolcriwd by tivci opposjtrly diiirgrd tracks in tlicccntral tratking dctcclor and 110 cncrgy dcposilioii in tlic caloriinclcr a i ' a r l froni l ha l of tlicdccay pions.
4.1 The Elastic p" Photoproduction Trigger
As mcntioncd in diaptcr 2.2.-I tlic ZEl'S tiiggcr l ins t lncc Icu-ls To triggcr clastic pn
Photoproduction rvcnts a dcdicalcd /) t i iggcr was dcvclopcd. Tliis triggrr dc r r i ands tlicfollowing rcquirctncnls:
• at llic lirst liM'd triggct (FLT) a l leasl l(j| ,Mc\ in t l ic e lcr lromagnrl ic scclion "f tlicrcar calorinictcr cxrl inling tl ic to\vers si irronndiiig llic hcainpipc (RK!lfC'n,i}. a t leastonc good track candidalc, Icss t l i an 12."»(1 McV in ( I re itmcrmosi ring siirromidiiig tlichcani-pi|)c of thc fonvard ralnrirncter (FCAL fJPn.i) and im vcto signals froni tlicZEUS vcto countcrs (sccfion 2.2.3). Tlic energics REMCn,, and FCAL ßPn.i arcnicasnrcd by tlic CFLT (scction 2.2.2).
• at tlic sccond Icvcl Iriggcr (SLT) Icss llian ~i OcV in tlic harre! and fonvard calorinictcrt;r, FCALst;r) and no liining-\ 'ct» signal froni llic ra lo t i rnc tc r ,
• at tlic tltiril lc\'d triggn (TI,T) l l ic fnll fvcnl i i i r r i r i n a t r o n orZRl'S is avaihilitc. Morrstringctit vct« ciits arc tipplicd. Tn sclcct pn p l in tnp in<l i ic t ion cvnits t\vn diircrcnt TLTtriggor strcnins arc nsrd. Dolli i c r jn i i c at Icast unc' trark p ' i inl ing tu ihc iittcrticLionrcgion and an cvcnt vorlcx in / w i l l i i n (50 cm aronnd tlic nun i ina l vcr lcx. Tlic niitnlicrof tracks has tu l>c Icss t l ian Fmir (TLT p triggcr) "r siv (TI,T w Iriggcr) am! llicinvariant niasN of onc 2 irark pair sniallcr l l ian l . f i (JcV (TLT /< Iriggcr) nr l l ic tolalin \ ;u inn t rnass .«maller llian 2.5 Gc\ (TLT u< triggct) Tlic niass ca lc i i l ; i t i i>n uscs [In-nionicntiiin nicasnrcniciit fnini tlic CTD assiiining llial all partirlcs arc pinns. In tlic1991 r n n n i r i g pcriod l«» ( l i triggcrs wcic prcscalcd liv :i f j i c t u r df six.
The cllicicncy of all llic triggcr ciits, cxrcpt tlic REMC,.,, rc(|iiircn»'nt, is \-er\i ;m<l f-jinIn 1 di ' lcniiincd fn in i Monte Cailo cvnts s i n n i l a l i n g /in p l iu lnprudncl imi (scrlitui ."»), w]n<;li
arr passed t h n m g h t In- ZEUS dclcrlor S imula t ion program MOZART, t l i c Iriggcr Simula t ionpnigratn Z G A N A and the n'constriiction program ZEPIIYR. Thc rcsnll dcrivcd from t l i rMonte C'arlu is comvl, if thc rlficirncics i" chiln arr reprodiiccd by llic Monltr Carlo. Toniakr snrc t l i a t l l i is is ihr casc al l ihr Iriggcr cnts arc cxaniincd, cxccpl the REKfC'n^f t ' t ju i r i ' i i i c i i l whicl i wil l bc discnssed in scction G.1 .1 .
All l l ic vcto tu t s arr cluiscn to rcnmvc rlcar barkgionnd cvcnts wi l l i a iirgtigiblr loss o f r prvrnts. Thc vclo cnts Jirc not simnlatcd in tlic triggcr Monte Cartu prograin. An outline. ofall t l ic vcto cnls follows
Tlic vclo cnls ;it llic FLT arc bascd on thc l iming in thc vrto comitcrs npstrcnni thc pnilonbcani d i r cc t ion . These t i t n i n g aits arr dioscn tn rcmovc obvions proto» bcamgas intcrac-tions. Al SLT and TLT thc calorimctcr is nscd to providc a vcto signal in rase of n clcarbackgroimd cvcnl. Nun r;; cvrnls can lic identih'cd by thc l i inc of thc cvcnt which is vcryprecisely incasnrcd by llic calorirnclor. ßy ihr cat ibrat ion, ihr inran calorimrlcr linic for ancvcnt o i i g i n a l i n g froni (lic intcraction poinl is /ero Upslrrarn proton bcaingas hitcractions,whirli arc tlic inosl scvcrc barkgronnd al llic SLT, havc carly [1CAL tiincs or big t i tnc dif fcr-cnccs brtwccn FCAL and RCAL. Sitnilarly upsireatn Hrctron beamgas intcmctions ran bcvctocd by an carly FCAL tinir . At thc SLT also cvcnts wil l i an nnphysically high valnc ofE - P, arc vctord. Events triggrrcd at FLT by noisc in a pttnto mulliplirr an* idcntificd atSt,T and TLT äs havitig a ccll willi largc rncrgy imbalancc, MIC diffrrencc in cncrgy bctwccnllic Icfl and righl plioto nudliplior, whilc thc rcst of thc ralor irnetrr is (tuict. Cosnüc mnoitsarc vctucd at llic SLT by Ihr Einic difTcrcncc bctuccii llic uppcr and Iowrr lialf ofBCAL. Altlic TLT, cosniic and halo innon cvcnts arc rcjrcted by niaking tisc of thc timc and positionoF i h r cnrrgy tlrpositK in thc caiorinictcr äs well äs thc TLT track and vcrtcx Information.Details on thc veto algorilhms wscd at llic SLT and TLT can bc foiind in [22] and [12|.
Highly prcscnlrd conlrol triggcr strrains, whicli nsc rclaxcd triggcr ctits can bc nscd todetcniiinc thc cflicicnry of llic trigger ciits in data Tliis pHicicncy das to bc comparcdto tlic rflicicncy obtaincd froni thc Monlc Carlo sininlal ion. If nrccssary, ruls on o f f l i neo,i tantit ics arc introdnccil in data and Monte Carlo rvrnls to gct good agrccnicnt in thctriggcr cfh'eiriTcies. Dala and Monte Carlo pvrnts arc comparcd aftcr sclccting pn candidatesby rcqi i i r ing cxactly two, oppositriy chargcd tracks froin a vcrtcx wi lh in ihrcc sigtna aronndthe niPiin vcrtex rncasnrcd in thc 199<1 running period (srctioti 1.3.1).
• Tlic FLT triggcr cnts arc studicd separatcly
- For the eilt of al least mir good Irack i andidatc, t l i c vcctor mcson conlrol triggerslreams can not bc nscd to dclcrminc the clficiency in thc data, since. all Iriggrrsre(|iiirc this conditioii- So an indcpcndenl oonlro! Iriggtrr, which dors not rc^inrctracking is nscd, in this casc tlic tatjqrd jiliotoprodiiclton trifjfjcr. This triggcrrcr|tiircs at tlic FLT a coincidcncc of an cncrgy dcposition in thc rcar caloriim-tcrand a lag in ihr elcctron detcrtor of thc luniinosity syslr.ni. Thc cHicicncy of oncgoofl track candidalc for llic sclrclcd cvents in data is biggor than 95% and agrcrsw i l l i thc Monte Carlo effidcncy within 2% aflcr applying cuts im the track (|iialily,nanicly tlic pscndorapidily |j;| < 2.1 and l l ic liansvcrsc nionicnluin Pr > 15(1 McVof hoth tracks (scclion 5.3) Tlic diffcrcncc bclwccn data and Motile C'ailo can bcnndcrstood froni llic diffrrcnt i; spectra oF lagged Jind fi° photoproduct ion rvi-i i ts .B\ r t i t in ing llic triggcr s i tnu la l in t i p roRrani Z G A N A on da ta llic rornx-incs^ nftlu- s i n i i i l n l i o n progratn is clicckcd äs \\-i-\\l t n r n s out t h a l t l i c s i m i i l a i i n M is
l- 'Ih
1
0.90.80.70,60.50.40.30.20.1
00
o
Figt i re4 1: Tlic f ra i t ion of cvcnts f n l f i l l i n g thc eil t FCAL nr^.t < 12ö(lMcV For t l ie ronlrolsample, (full <lots) and a proton dissociativc Monte Carlo sample (open dots) äs n f i inct ioi iof thc ciicrgv in FCAL in tlic two inncrmost rings snnoimding ihe bcampipe.
corrct't w i t h i n 1%.
- Thc cut on FCAL DPn,i doc-s not »ffcrt cla.slie /)" pho lop iMf l i i c l i i in c\eiits sincctlic trans\crsc niomciilmn of llic scaltercd prolon is loo small l o rcacli llic forwardcaiorinictcr and the calorimctcr noise is inncli sinallcr than t .2 dA'. Rnt fur prolondissoci;iti\ p" photoprodiiclion, in whrch ihc ontnoing liadron is cxcilcd in t o astatc M K, encrgy can be depositcd in t l i c forwatd calnr i rnr tcr A rotitml strcarn,whicli d i f fc ' r s froni llic p trigger by Ihe ml F('Al, HF,,,, < .'tdOO Mc\ is itsefl 1ocompiirc dala and Monte- Carlo Fignrc J l stinws the naclion of event.s f n l f i l l i n gtlie eilt FCAL BPn.r < 1250 McY for ihr conlrol sample (fnll ilots) ; in<l a prolondissociativr Monte Carlo sample (open dols) äs a Fnnclion of tlie eiiergy in ihctwo innertnost rings siirroniKting thc beampipc F.,.,- \ H f2 , un-asnrcd oHlinr. Tliefraction of cvenls vetoed by thc cut FCAL R PH t < 120(1 McV riscs slowly andreat'hcs ~ 5()^{, for 3 Gc\'. To obtnin a good agreemetit bctween dala and MonlcCarlo sä m plc a cnt on E^^AI. nr-i "' ' 2 G(A' is inlrodnced. As al icady mcnt ior icd ,this eilt has no elfcct for clastic /i° plio(oprodii{-tion cvents, bnt is impoilant inthc stiidv ofproton dissocialive p" photopro<lnc1ion (scction 7.4).
Thc dliciency of the SLT cncrgy cnls is deteniiined bv nsing a cnntrol Irigger stream,whicli is idcnlical t o tlic p trigger, bnt has no RLT cncrgv cn t . On top of Ihe seleclioncnts mctitionrd abovc, clastic p" pliotopiodnclion cvents arc sclccled by rc ( | i i i i ing l hatin tlic ealormiclcr no cnergy deposilion above noisc aparl llic mir fiom ll ie decav pions(seclion 4 3.2) is fonnd. After applying l l i i s ciil the SLT rnergv d i s l r i bn l ion for BC'ALand FOAL peaks well lielow ihc 5 GeV. Tlie nuixinniin SI,T cncrgy in data and MonteCarlo is aronnd 3 (ii-V. Also for prolun dissociative rvcnls ihc SLT energv cnl in FCALlias an cdiciciicv of 11)0% sinrc ihr FLT <-nl on F ( ' A L W / V / . ; 's already ( igh ic r . Soihe SLT encig\s have an efficicin-y nf 100% in dala and Monte Carlo sample.
(,'fi.i;»(i'i l. kVrul Si'hf
• Thc TI,T trat kirig nils an1 stndicd wjt l i n rontrol iriggcr strcam whirh docs iml icqiiireans TLT tiacking For data and tlic Muntr Carlo sample tlic number of trarks fonndjit ll"-' TLT is lowcr than thc tiumbcr of trarks foimd offline. Sinn- ollline two twksair reqnircd, tlic nppcr limit un tlic imiiibcr of trncks al tlic TLT das an cfficicncy of100%. T wo prescaled triggcr strcjiiiis arc uscd at tlic TLT whitli have difFerenl rnts011 thc invariant mass To add up tlic cvcnls frmn bolh strcatiis in onc analysis it hasin bc nssuml tltat ihr two strcams acccpt p° cveuts with tlio samc cfficipncy. So thcfractittii of evcnts, \vliicli are triggcrcd cxclusivcly by onc triggcr strcam, is dctcrmincd.After applying a cut 011 thc invariant lw» track niass, cahrtilatcd offline, of M,tt- <1.2 Gc\ is inlroducrd only k-ss than 0.01% of tlic t-vcnis takcn by tlir p triggcr arcnot triggcrcd t>y tlic ui triggcr anct 0.27% (>f tlic cvents takcn by thc u triggcr arc nottriggerrd by tlic p triggcr. Thc diffcrcncc in thc triggcr cfficicncy bctwccn tlic t wotriggcr strciiins incrcascs with incrcasing inass and bcconips sizcablc abovc 1.2 GcV.So thc analysis will bc rrstrictcd to M.t.- < 1.2 GcV. A vcrtcx at thc TLT is onlyrcctinstnictnl. if at Icast onc track is pointing to tlic intcraction rcgion. Thc cffiriciicyoT thc at Icn.st onc TLT vcrtcx track and a TLT cvcnt vcrtcx in 7. within 66 cm iiroiindthc nominal vrrtrx is biggcr tlian 98% for thc sclcctcd cvents and well rcprodticcd bythc Monte Orlo.
As alrvady nicnlioncd thc two TLT triggcr strcatns uscd in lliis analysis arc prcscalcd. Forcarh physics rnn tlic prescalc factor can l»c dctcnnincd, sincc in thc run summary thc ntinibcrof cvents fnlfilling thc triggcr Nt„, nnd the nunilnT of cvents takcn by this triggcr aftcrprescalc N,otf arc rmirdcd. Tbc prescalc factor is given by P = Ntr,9INtake. A corrcctionfactor for thc prescalc corrrclioii of two triggcr strcanis can bc dcfincd äs:
l lp p i • •'
r ' p triyyfr l u triyyri
To corrccl for the prescalc factors thc luminosity for each physics run is multiplicd by itscorrcclioli factor C.
In tablc 4.1 thc elh'cicncics of thc triggcr reqnircmcnts, for p° candidatcs (two oppositclyehargcd tracks froni a vcrtcx}, äs dctertnmcd froin control saniplcs and a Monte. Carlo Simu-lation aro summari/ed. Tltc efh'ciencies are closc to 100% and agrcc vcry well bctwccn dataand Monte Carlo aftcr applying thc extra sclcction criteria.
triggcr
ret|llircilU'ltt
FLT: good IrackFIT: FCAl DP*,,,
SLT: DCALs,.i, FCAlsuTLT: niultiplicily <'»lTLT' vcrtcx nitTLT: niass cnt
eflkicncy
froin data
95%100%
100%
100%
98%100%
cfficicncyfroni MC
97%100%
HH)%
100%
99%100%
extra sclcction
critcria
|q| < 2.1 and P, > 150 McV
EfCM.nn < 12 GcV
A/...- < 1.2 GcV
Tablc 4.1: Triggcr cfh'ciendcs for p" candidntes in data (control sample) and Monte C'arl".Thc exhn selcction critcria have tu bc applicd to gct a good agrecmcnt bctwccn data andMonte Carlo.
4.2 Reconstruction of Kinematic Variablesr
In scrtioii 3.l the kincmatics variables desi ribin^ p" phoiopindiirtion arc inlmilnced. Sinccfor this data sample only thc decay pions of tlic /'° are incaNiired in llie ZFL'S deleclor, thckincrniatic variaMc-s ha\x' to bc reconslrürted finm tlic momenta nf the pions.
The sclcction cuts rcjcct cvents in wliich thc scattcrcd cleciron hits Ihc ZEUS calorinietcr.Thisrcstricts^lobcbchnvf^ as-lGcV. The minimal Q! is givcn by Ql„„ = Ä/,V/(l-V). For QJ = Q2mn thc vjrtnal pholi.in has /.cro transxciw inomeiKimi and the lotigitndinalmomcntuni P,-, can bc approximated by -£-,, sincc (^2,liri is of ihc onlcr of l()~9 GcV'2 inthc kinematic ränge undcr sttidy. Energy and inonienlnin conservatitm rcads:
E, + E, = Ef' 4 E,, (4.2)
Subtracting cquation (-I..1) from (4.2( yields:
E, - rn = 2l-, x E„ - /'„,
sincc Ep w P,p and Ep< v P.p..
Thc photon-proton ccnter of niass eiiergy can mm be exprcsseil
(4.5)
Thr cncrgy F,f is givcn by £„* + E,- and P.,, by r,,t + P.„ . Tlir nn-igirs of llic pions arccalculalcd fruni thc nirasurcd tlirci1 momenta in thr C'TD iissiiining [In- track.s arc pions.
Thc four-nioineiitiini transfcr / at llii- proton vcrtcx in (In- ;d>u\ apptoxiiiijilion (Q* ^ I),P,-, — ~E-,) is givcn by:
- -P2'Tp
As can bc SITU frnm this dcrivation für nun ?cru Q* Ihr rcrmistiiK-lrd P;2 will dilfcr froin— t. This eifert will bc disrusscd in niorc dctail bcluw.
Thc dccay anglcs in the hclicity franie, dcliticd in scctinn 3 .').!, im- also rr-conslnirtcd in tlicabovc approxiination. A photon virtnalily nf Q"1 ~ 0 and n» Lransvcrsc riioiiinituin for thcphoton and tlic iiitoming proton an- assiinicd. In lliis iippru.viiiiiitioii only l wo anglcs canbc rncasurcd, naniely ßh and <ph- ^ deh'ncd äs thc angle belwrrn tlic Icptun scattrring andUic production plnnc is not mcaMirable, sinrc thc Irpton snillrting plane j.s inidclincd in thisapproximation.
Tht'Stncaring in thc kineniatic variables and the dccay anglcs, dnc to tlic dctednr resolut tun,is dcterinincd froni a Monte Carlo Simulation. Events siinnlaling einst jr pn pliotoprodnrtiunarc possed throngh thc ZEUS dctcctor Simulation program MOZART, Ihc Iriggcr Simulationprograni ZGANA and tlic sain<! icainstMieliun pmgrain ZF.PIh'R äs thc (|al;i. Radiation of
0.5
0.4
C 0.3VO*Q.
0.1
80 100rec. (GeV)
0.2 0.4P? rec. (GeV3)
cos6h rec. rec. (rad)
vP. 1
0) 0.8D>
E 0.6
0.4
M.«, rec. (GeV)
Figiuv 1.2: Corn-liition bclwrcn tlir irconslructi'd und llic guneratrd valuos für ihr kinrmaticvariables and die drcay anglcs-
1.2.
-0.05
1000
800
600
400
200
0 0.05,„.-M.t:. (GeV)
.1 -0.5 GeV
-0.05
M.
'-0.05 0 005M.„_-M.t7- (GeV)
M.„. : 0.7 - 0.9 GeV
300
250
200
150
100
50
0
0 0.05M.«,-M.tr. (GeV)
: 0.5-0.7 GeV
-0.05 0 0.05U -M.r:. (GeV)
M.,.. : 09 - 1.3 GeV
Ftgiirc -13: DilFt-rciicT lictwccii tlio rccoiiKlnirtcil nnit Rcttruilcil tnnss l'i»r (lilFcrrnt innss liins.Siiprriinposrd is llic rcsnlt of a lit with n dnnlilr C!ftiissi;iii ( -17)
rrnl (iliotons Froin tlir iticnniing (»r oiitgoitig Hcclron is rml iiu'lndcd in Mir .Simulation(scctioii 5). Tlir .snicaring tlcUTttiiiicd l>y cn[ii|iaiing tln1 Rcnrrsil«'»! ;itul thc tfconstnulcdvalurs of a kinrnuilic varialilc inclnilcs thr cffiTts oF tlir dctcclur rrsoltilinn ninl llir appiox-itiiMtioii givi'ii abovi1. In fignu1 4.2 Ihc grncriitcd versus tlic rccnnslrnctrd \\'-,,„ T/, cosfl,,,(fth and jl/,4. - nri1 shcnvn A gtiofi currclation lictwccii ihr grncralrd and thc rrrnnslrwlrd
valncs is srcii. Tu litok closcr at llu1 smcaring, Üif rcsolnlimi, di'fiiicd äs dilFi-icncr lichvccnrrronstructcd nnd gcurrotril valncs is stndird As an cxainplr (ignn- -1 '\s t|u< n-scilnlion
in inass (M,t.- - A/'VJ,-). ^(tr tlifFcrcnt Mus in M,<r-. Tlir iTMilirlimi can l»1 wi-ll rtcsrriljcdl>v a douhk1 Ganssian ttf tlir Form:
/(A/.,.. -A/;V..) =
„,-JP^JF^ 4-7)
C11 .'1 J > l iT -I.
11\, liin(GcV)ÜU-KM)
50-GO
GO-70
70-RÜ
80-100
r,{McV)
-2.2-2.7-2.G-1.7-1.8
P3
(McV)7.4C..I8.G13.733.6
tf
0.390.340.711,79O.Ü
/V(GcV-1)
0.150.270-581.490-0
n1(McV)
15-04-0-6.0
17.00.0
n14.021 038.01G.O0.0
Tablc 4.2: Tlie panimctrrs dcscribiiig tlie mass rrsulntioii in diffi-rcnt U'1P hins according to(4 .7) .
As a rrsiilt of n lit wilh this functinn it is found ihn t ihc rrconstrurlcd ituiss is shifirdversus thc guiitjralcd ono by -2 Mi-V. Tlir- Kontr ibut ion uf die sccond Gatissian P^ is nonncRligiblc. Tlic signia of thr clominating Gaussian Pj(= o\t t _ ) is on the ortlcr 7 McV.Thc pnrnniclcr ^ dccrcasrs äs a functinn of A / » » , - and P-3 incrcasc äs a function of M,*,-.Tliis dcpuntlrncp ran bn paramr(cri7cd by linear funcLions P, = P,' - f^A/»+»-|GcV]) andP, = Ps' + PjA/. + .-IGcV]). Tlic mass rcsolution was also studicd äs rnnrtion of U'1P, P,2,cosfft, and ,. Tlic mass rcsolution incrrasos äs a fuiiction of H'lp but MO dcpcndcncc isst'cn on Pf, cnsflft and fa. Thc parflinctcrs (P? to Ps) dcscribing thr mass rcsolulion arpsiHTiiniiri^cd in tablr 4.2 for thc H'1P bins, uscd in this analysis. These rcsults w i l l bc tiscdlatrr in tlic analy.sis of thc fl/^*,- dislributions, whrn thc: corrccted mass distriblition isfit (cd by a convolution o f thc thcorctical niodcl and rqnation (4.7)- The increasc of ihr massrrsotiiHon for iiicrrasing H",p can bc tindcrslood front thc fact that at Iow \\\ thc tracksare «•<-ll mcasurcd in thc tracking chanibcrs and for big H^p thc tracks arc sliort, so thcrcsolution is worsc. A simtlar cifrct is sern in a,,i, whirh also incrcases äs a function of I1'1P.
Tlic tlccay angnlar distribntions cos^ and <f>h «"il! bc studicd in this nnalysis äs functitmof /U,*»- and Pf. Thc rcsolution in cos9h and <j>h dccrc.-iscs äs ^/w*„ incrcases. On thcoMicr hand nrfnt^ shows no drpcndcncc on Pj, bul n^ incrcascs for tlccreasing Pj. Thisis oxpcctcd sincc fnr srnall \1\c pruduction plane is badly nicastirod and for t = (,,„„ thrplioton and Ihc f>° arc collincar, so d>h is undefined.
The rcsolnticm in Pf. and II',p is studicd äs well, but for thc rcsults prcscntcd in chaptcr 9only corrected jU,».-, cosfl/, arid $,, arc nccdcd, so thc fociis is put on thcse variables. Nosystcmatic shifts bcUvccn Ihc gcncratcd and thc rcconstmctcd variables arcsccn for P,2, II\,cnsöj, and fa In tablc 4.3 tlic typical signia pj ofthc dominati i ig Ganssian in all variables islistcd togcther wi th thc bin width clioscn for thcse variable in thc fürt her analysis. Thc binw j d l h is always choscn to bc biggcr than thc rcsolution in the all rcgions, of thc kincmatic
quantitv
^„.*-cos eh
*$";„
signia of thc Gaussian7 McV
0.040.20 rad
0.001 Gi-V0.3 GcV
bin width in thc analy.sis25 McV
0.08n/10 rad
> O.OOG25 GcV3
2.0 GcV
Talile l 3; The rcsolution, drfiiicd äs llie signia of tlic dominat i i ig Gaussian and the chosenbin widlhs for thc kincinalic variables and the dceay anglcs.
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Fignre 4.4: The correction function uscd to convcrl Mie mcüMircil Pf d is tnbnt io t i lo a \t\. Thc correction iiu-rcascs for inciejising Pf.
variables, undcr study.
As alrcady nicntioncd abovc, ~Pf is nscd äs a ineast i i i ' of I. For non /rro Q'1 Ibis iipproxi-inalion wil l bcconic worsc for increashig Pf, bccansc big Pf <;;in br caused by |/| or Q7. Thrmcan differcncc betwccn Pf- and \t\i bc trnnslatrd in a rornvtion fiinetion F ivhicli has(o bc a[>plicd to l he Pf dis lr i lmlion to gel die \l\. This cnrrrction fmiclion isdefincd äs
_ gcneratcd c\-enl,s in Pf
= ^^cTaTT^WtTnTTn (*' 8 >
and is cvalnated froni thc Monte Carlo, assiiming t ln- Q* « l i s t r i ln i t ion gi\vn by (3.53). Infignrc 4.4 thc fun r t i on F is sho«-n versus Pf Tlir n u i t v i i o i i s tar ts tu bcroinc big abitve0.5 GcV2 so this analysis is rcstricted to Pf < (15 GeVf The corrcelion fmirtioii F t.sdcterniincd for each scli'ctcd rcgion of k in rma l i e \ari;dilcs niidei s tudy scparaldv.
4.3 Selection Cuts for Elastic pi] Events
Ehislic p0 photoproduction cvcnts arc d ia iac te i i^cd in Ihc ZEl.'S di'trctor by l wo ehargedpions in thc ccntral tracking chainber (CTD) and no energy di-posilion in the caloriinetcr(CAL) apart froni Ihc onc from thc pions. The selcclion culs inakc usc of this chara< itcristic.
4.3.1 Tracking Cuts
Thc rlficiency for sclecting cveiUs w i th cxaclly (wo Iraiks (lf o]>pusiLr rhargc poiming in ihr\er tcx is calculatcd froni thc Monlc Carlo sarnj i lc To gcl ;in idr-a of die incff inci icv of this<-nt !hc fol lowing four classes ofevcnls in n control data sample arc considcred.
• (1) p° cawtidatcs. nainely esaclly hvo trarks of oppnsilr chargc poiming |M thr vrrtex,
• (2) (wo tracks but only onc (rack is poinhng lo die M-KCX,
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Fignrc 4.5: Invariant mass distrihntiuns for pn candidatc's (nppcr Irft plut) and rvnil classi«(2) to (4) dcfincd in tho tcxt (nppcr riglit to towcr riglit plot). For p° candidatcs a clcarmass pcak is scrn.
• (1) additional tu llic t\vo vcrlcx Iracks a lliird track is fotind,
• (-1) cxarlly two Iracks fnun tlic vi'rlcx Inil of ihr sainc thargc.
In ligtirc 4 5 tlic invariant niass disli ilnilioii for thc control sample is sliown for llic fön r cvrntclasscs. For class (.'!) tlio mass is talculatcd froni thp two vcrlpx tracks. No clcar fi° signalis sccn for thc cvonls which fail thc p° sclcction culs slightly, hui a clcar prak at tliu propermass is sccn for thc p" candidatcs Froiti llic nnnilicr of cvcnls in cach figtire it is oh>-io«sIna! tlic prubability for a p° rvcnt lo fall Ihc tracking cuts is sniall. In tablc 4A thc mimhcrof cvcnts in thc classcs (2), (3) and (A) dividc-d by thc nnniber of cvcnts in class (1) is givcnfcr dtita nnii Monte Carlo sample. Tlic rat ins arc givcn for a srlcction bascd on thc trackmiilti|)licitics (track sch-ction) äs cxplaincd aliovc and for an clastic sclcction, whcrc on topof Mir tratk sclcction no significnnt cncrgy dcposition in thc calorimctcr oiilsitlc tlu1 tracksis allowi'd (scction 4.3.2). For llic l nick sclcclion maiiily background cvcnts arc sclct-tcd in
toi Hi\atH-
cliiss(2)
d;iss(3)dass(4)
datit froin a runtro] sampletr;ick sclection0.139 i II Illtt
( ) . 1 ( H ) ± O.OOr»
0.1)54 ± 0 0 0 1
clasjic selcction0.008 ± 0.(H)2
0.0 10 ± 0.00-1
0.011 i 0.002
clastir p" Muiltc Car lol rack sclcclinn
0.081 ± 0.008
0.02G ± o.oo;.0.008 i 0.002
claslic st'lcdioii
O.OIß ± 0.001
0.019 i 0.001O.OO.'i ± 0.002
Talilc -1.4: The ratiu of thc nuniber of cvcnls in classcs (2),(.'i) iind (4) n\rr llic iiinnltrr oFcvctits in rlass (1) furdatü {coiitral stiittplc) fitnl clastic f>" Mnnlc C'arli) fin t In- Irack sclcclioii
imly and Tor track plus rlastic cvcnt s
if.it a, ns is shown l»y thc invariant tnass distrihnttuii, whidi nie not siinnlah'd liy Ihc claslitp° MniitL1 Carlo sample. TliciTfori' thc nitins in tlatn arc ninrh bi^RfT tliini in tlic MonteCarlo. After applying tlic clastic srlcction ih'1 rcniaiittng cvi-nts in rlassi-s (2), (3) ;unl (4) inHata arc likoly l<> In1 clastic fP rvnits, which fiiil llic srlrction (1). Tlic ratius in datji ;iiulMontr Carlo sntnplc aftrr llic rlastjr sclcrtion arr Ihcrrforc ninrli rloscr. Froin lüblc <\.4 itcüii lir concludcd that tln- prohahility fnr an claslii- /i° cvcnl lo fnil tlic n;uking nils is snialland thc inrffidrncy is sufficicntty well irpindnrcd hy tlic Monte C'ailo.
As ülrrady mcntinncd prcvionslv n eilt <m tlic n-coiisinirlcd \c r tc \s appliril PiRiirt1 4 G
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10000
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20000
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Sigmo 11. l B
-60 -40 -20
Figiirr 4.G: Vcrtcx distribntions in x (tippn Ic'ft plol), y (nppcr right plut) and / (tuin-rin dala for all p° cnndidiitc? Tlic rcsiilt of a fil \ \ i th a CJanssiiin is supcriniposcd
sliows the measured vcrlcx distribulions in x, y and t. for all sclcctcd /i" cnndidalcs in thcselectcd runs (scction -1.4) A Gnussinn is fillcd to lliis distiibutions and thc mean vcllcxPosition foimd lo bc displacrd, for cxatnplc in / by 4.1 crn. Events \vith a vcrtcx inside tlircesigma are seiet l cd, so thc vcrlex eilt rcads:
H", - 4 0 7 c m | < ,1 II 18crn
HJ-O. I5c in | < 3 .0 .21 cm
|i; + 0.13cin| < 3 0.21cm.
The rnts on tlic vrrtcx distribntions in x and y rcducc the data sample by ~-2.5%. In thcMonte Carlo Simulation, vcrtcx distribulions in x, y and /, arc uscd at gcncrator Icvcl, whichwas dcrivcd front an unbiascd 1994 data sample'.
4.3.2 Selection of Elastic Events
Elast k cvcnts arr sclcctcd by rcqniring (hat ihr rncrgy in t ho most cnorgrtic calorimctcrrHI not assigncd to ihr tracks is bclow an cnergy vhiclt is givcn by thc maximal noisc intlic calorimclcr All calorimetcr cclls in tlic- elcctroniiignclic and hadronic scction of Ihccatorinicter inside a circle nround Ihc Irack impact points arc assigncd to thr tracks. Thcniost cncrgctic teil in räch calorimctcr scction aniong t hose, wliich arc not assigncd is iiscdin tlic sclcclion eilt. To sclcc.1 claslic cvcnts wilh a high pnrtty and and high effirtnicy thcradins of the circlc and thc noiso in tlic calorimctcr havc to bc dctcrmincd. Thc noisc in thrcatorimctcr cati \w sludied by üsing random triggcrcd evnits. Tlicsc c\ciits arc takcn dnringllu- nsnal dala taking wilh a rate of (1.03 Hz. Tlicy arc passcd Ihrough all triggcr k'vrlswithont any triggcr cuts and nronstnictcd likc nsnal cvcnts. Sincc thc probability ofliavinga pliysics rvent in a randomly triggcrcdcvcnl is almost /cm, thcsc cvcntscan bc uscd lostndythc noisc in tlipdctcctor duringrlata taking. Tlic noisc in thc cnlorimrtpr isstndicd scparatclyfnr thc tlircc diffcrcnt calorinictrr parls (RCAL, DCAL, FCAL) and Üie ck-ctromagnelic(BMC') and hadronic section (HAC) Figurc 4.7 slunvs thc cncrgy dislribution of tlic niostcncrgi'tic calorimctcr ccll in randomly triggcrrd cvcnts
Dnring tlic rernnstruclion ;in cncrgy thrcsliold is applir-d to tlic cncrgy in cacli calorimctcrccll. So cnrrgim bcliw GO McV (EMC), HM) McV (HACO) or 110 Mr.V (HAC) arc sei to zi-ro.This culs out thc vory low cncrgctic pari of thc noisc spcctra. Ncvnrthcless it is obvious l hatihr noisc sppclra fall off vcry fast. This is rxpcclcd sinco thc dominant sourcc for noisc arcradinactivc dccays of thc dcplclrd tirnnititn and clectronic noisc. Frora thcsc plots thc cittvalncs fnr tlic most cnc.rgctic teil apart froni thc tracks arc dctnrinincd äs listcd in tablc 4.5.
calorimclcrscclionR.EMCRHACBEMCFEMCFHAC
niost cncrgclicccll tut (McV)
< 1GO< 200< 240< 200< 240
ineliiticncy ofthccul (%)
0.040 .110.050.150.30
Tablc 1.5: Tlic most cnergclic ccll tut dctcrmincd front ranrlomly triggcrcd cvcnts in Ihctlircc raloiimctcr parts The ineHicirncy is dctcrmincd front data.
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Figurc 4.7: Energy of thr niost cncrgctic ccll in randorn trißgcrcd cvcnts, in thc drdnnnag-nctic (Icft plots) and thc hadronic scctiinis (riglit plots) of thc calorimclcr-
Thc iiH'ffii-ii-ncy of tho cnt is givcn by t In1 nninbcr of cvnils in nitirlum triRRcrnl cvrnts alinvcthc tut ovcr all cvcnts. A tut on thc hadronir scctinn of thc baiti1! calorimetcr (RHAC) isnot applicd in (Ins analysis sincc all ncnlial partirlcs coiiiing finin thc inicraction rcginnhavo to pass throngh itic clcctromagnctic scction (RfCM(') lirst and thrrcforc a tut on llicmost rncrgrtic ccll in BEMC is snlHcicnl to sclrrt clastir ff* rvenls. In llic 1!)94 d;i(;i takiiigpcriod somc caloiiinctcr cliaiilicls showcd addilion.nl noisc visiblc ;is t aus in llic noisc spc< tra.Figurc 4.7 shows tlic noisc spcctra after correclmg for lliis cxlra noisc. It tnrns onl that lliisadditiimal noisc shows up only in a sinnll nntnbcr of crlls. Sonic of llicsc cxlra noisy ccllsarc rcmovcd by cnlting on thc absolute valnc of ihr relative Jmhalanrr {< [).7) i thc absolute\aluc of thc diffcicncc in thc cncrgy tni-asnrcnicni (1111» llic Icfl and righl photo miiltiplierdividcd by llic surn of llicsc cncrgic's for a teil. This ml is applicd to isolatcd cclls witli ancncrgv bclo« (J.7 Ge\ only. Tliosc noisy fdls, whirli fnllill ihr itnbalam-r rrilerion arc wellideittificd by thcir occnpancy äs niost cnrigcijr cclls in ramlom Iriggcrcd c\cnis. Il htnis
1
0.8
0.6
0.4
0.215 20 25 30 35 40 45 50 55 60
1.1
0.9
0.8
0.7.
g 8 § § 8 8 8
35 40 45 50 55 60 65 70 75 80 85RH« (cm)
Figurr 48: Effitiency of tlic cnt on tlic most cncrgctic ccll away from thc tracks, äs afnnction of Ilic railius around tlie trark irnpacl poinls, for p° Monte Carlo (fnll dots) and uMonte Carl» {npcn (lots) cvcnts. Tlic uppcr plut shows tlie clficicncy for diffcrcnt radü in(hc clcctromagnctic scction and tlic Iowcr plol für diffcrcnt radii in tfic liadronic scction. Inllic Iowcr plol a cnt at RKMC = 40 cm is alrcady applied.
o« t tliat llie.se cxlra noisy cclls or hol colls oiily sliow np in parts of llic r u n n in g pcriud. Theoncrgy fbr tlicsc teils in thc affccted rnn ränge is sei lo zero, if il is bclow a ccrtain ihrcsliold.Tliis llircsliold iiiintmi/cs tlie loss nf physics and is givcn l>y tlu- highrst ciu-rgv' dcposit inrjiiKioinly tripgprrd cvcnts for cai-h hat ccll. A list of all hol cdls with tlic corn-spondingiipprr rncrgy cnt and thc affcclrd nin ränge is givcn in Appendix A. Sincr in thc dotcclorsimntntion only a paramctcrization of llie radioactivc dccays of tlic uraniuin is nscd and holcHls arc not simnlatcd, tlic inefftcicncy of tlic cnt on tho inost cnorgctic ccll is bclow tlicinrifirieiicy cstitnatcd frotti dala givrn abovc, Imt llic rffcct is sinall.
Now ttie siür of tlic circlc aronnd tlic track impact point lias to be fixrd, A diffcrriil si7o isnscd in thc clcctrumagnctic and liadroliic scction of tlic cnloriinctcr taking tnto account lliodiffcrcnt radial si^c of tlic showcr at difforcnl dcptli in tlic calorimctcr. For llic slndy of llicsi/,c of tlic circlc Monte Carlo cvcnts simntating chistir p" photoproduction cvcnts äs well äsclastic u,1 pliotoprodnction evcnts (in thc dccay niodc u -* Ä^n'Tr") arr nscd
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Afler sclccting t wo track evetits Mir radii of llic circ-lcs nronnd thc trark inipact poinls ;in-varicil for thc clc-ctroinagnctic and thc hadionic scction scpjiralcly. Fignrc 1.8 slmws llic cdi-cicncy of tlic cnt for düfcrcnl radii in thc cleclmmagnctic and tlic luidioiiic scrtinn fnr p iinrlu cvcnts separalcly. Tlic c-fficicncy of tlic cnl in thc cIcctroniaRiiclic scctinn (nppcr plol) forsclccting p° cvcnts dcpcnds for sinall rndii stnmgly 011 thc radii Itnl for radii abovc •!() crn lliccfBcicncy is alinost constant. A high clficicncy for sclccfing rlastic /'" pliolopioduclinn cvcnlstogcthcr with an acccplaMc rcjcctioii against backgronnd frotn clastir w pliotoprodiictinn istlicrcforc found at a rndiiis of 40 ein in EMC. After applying thc cnt on tlie chrlioniagncticst'ctton, tlie cfficicncy for sclccting clastir cvcnts is abnosl indi'pcndcnt of thc si/c of ihrcircle in llic Iiadronic srction (Iowcr plot in fignrr -1.8) Thc si/c oflln' cirrlc in ihc hadronicscction is clioscii to bc 5Ü cm to gct an rflicicncy bigg'-r llian 98% Tor tlrc pn Monte Carlo.Fignrc 4.9 shows tlie cfftcicnry of tlie eilt for dilfcreiit radii of tlic rirclcs in thc data. Il isobvioiis that for biggcr ra<h"i thc anioiinl of liackgronnd in data bcromcs liingcr sinrc Uic cdi-ucncy dotrs mit Hatten like in thc rase for llic clastic /)" Monte Carlo. On llic ollici liand thcincicasc in data is similar to thc inrrcasc in thc clastic u Monte Cailo. So Monlc Carlo sam-plos tan bc nscd to estimalc tlie anionnt of liarkgioiind in tlie incasiircd p° sigiial (cliaptcr 7).
4.4 Selection of the Run Range
For ihr iinalysis prrsenlrd hcrc otily thosc runs, from tlir 199-1 data taking poriod, witlinominal vcrlcx and positron beani arc usrd Runs fruni tlic elcrtron running pcriod in 1991
are not uscd sinrc tlic CFLT was not calibratcd for llicse rtins, which rcsnlls in n Iowcrrlficirncy of tlic REMCn.i cul Runs takcn aftcr thc shiflcd vcrtcx nins arc also rcjrctcd,
bi'raiise in thcsc. nins extra noise in tlir furward calorirncter showd u p,
T wo selrction critcria arc imposcd on Ilic remaining runs. A run smnmary must liavc brrn
creatcd and tlic liuninosity of Ihr rnn has to bc biggrr thiin 50U (ib~'. Thr sccond sclcctiunmakes su n- (hat cach run has a rcasonahlc slatistics for l In- study descnbed ticlow.
To selrct ihosc runs for wliicli tlic ZEL'S dclcctor was running stahly thc mean and RMS
valurs for cacli run for thc followingdislribtilionsarc dclrrminrd: cncrgics in R EMC, RHAC,BCAL and FCAL and niimbcr of l>its in tlir CTD für cach track in thc axial laycrs, stercolayrrs and z liv timing laycrs. A rnn 7 is rcjrctcd, if tlir following critrrion is fulrillcd for tlic
distriliution in variable A:
\ ( ( A ) ) a l l r a „ , - ( A )3(/?A/5(.4})a„r„n)
(4.9)
(.4) is tlic mran vahic of thc dislriliutiun. Thf nican valncs ovcr all runs (((A)}ailtvn,
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run number
4.10. Nnmber of cvents per liirninosily aftcr all srlrrlion eiits for llie sclcctci
I I .SVIci-liMii » f t l u - D m , lt;it,, l!)
VJ
"cv£80009)
7000
6000
5000
4000
3000
2000
1000
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2
M.„_ (GeV)
Figurt- 4.11: The /in signal in tlic 1991 daia, aflci all sdertinn nits, foi \\\,, lictwcrii 00 ,im1(H) Gc\'. At low inass tf> niesons in the drrav channd A * A ~ arc obscrvcd.
and (RMS(A))attruns) arc dctcrnitncd liy fits «ilh n Gan.s.siari lo tlic rlislribntinn of (hctucan and RMS valucs of all runs. T wo itidcpcmli-nt TI,T triggcr strcams arr nscd, so l\volists «r iorfnms arr errat cd. Coniparing tlicso Itsis, i t tnrns mit tliat niost kad nins sliow u pfor both triggcr sticams and tliat thc bad nins arc grnnpcd. So ahvavs all runs in a singlrHERA rlcctron fill arc cxcludcd, if onc of llic riin.s in tlup Hll is idcntificd äs a bnd rnn. Tlicfoinplctc Hst of all nins cxcludcd frolii llic analysis uan bc found in Appendix B.
In fignro 4.10 thc ntimbcrofcvciits per Iiiminosity versus rnn niiinbcr is sltowii for ttii'sulrctrdnins. Thc mmilicr of cvcnts per liimiiiosity is Hat ovcr tlic selcctcd nins.
Thr clfcctivc inlcgratcd luminasity of thc sclcclcd sample, corrcctcd for thc Iriggcr prcsnilcfactors (4.1), is C = G91 ± II) nlr1.
Figurc 4.11 shows the rlasttr p" pliotoprodiiction signal in die 1991 in thc IIr,p ränge brlwecnj() and 100 GeV. Sincc the l wo trai:ks arc assnmcd to bc pions, backgronntl frotn cla.slic 0photoproduction witli a <|pray ofthc tf> in a h'*l\'~ pair ran l>csccn in thc dala at Imv A / „< , -
(section 7.2). To rc-dnce this barkgrunnil a tut of Mh>K- > I"38 GeV is inlrodiiccd Aswill bc shown in scction 6.2 thc acccptancc is vcry small for low invnrinnt masscs ftf,t, • .soIhc analysis of jf1 i)hotoproducliun is rcstrirled to A / Ä + .- > 0.55 GeV. In total 79010 t'vrnlsa r« Icft aflcr thcse tnts
I. f-.Vrnl S,lii-tion
Chapter 5
Monte Carlo Simulation
The resolution und tlic acceptancr of tlic ZF,ÜS dctcctor fnr claslic p" plmtoprodnction andthe for nackgronnd proccsscs to tlie rlasttr />" signal \verc Mndicd l>y means of a Monte CarloSimulation. Events simulating tlic proccss utidcrstiidy wie goncratcd using llic Muntr Carlogcnerator DIPSI, PYTHIA t>r EPSOFT (tadle 5.1).The gencratrd rvcnts wcrc piisscd tlirouglt a dctailcd siimilntion <iT th<' ZEUS drtrctor andIriRgrr. All piirlick-sgencraU-d at llic r;» vcrtcx arc trackcd lliroiigli l In- npparatiis, simulatingthc processts associatcd «ith thc passagt1 oT particlcs tlirongh matter, iising llic progminMOZART. Thc ZEUS triggcr is siniulatcd hy tlic program ZGANA. Tlic onipiit funnat ufMOZART and ZGANA is vcry simitar lo that öl ihr data, so Monte Carlo pvrnts can bcpassnl through thc samc ruconstrnction pvogram (ZRPHN R) and analysis prfigrani äs llicdata.
Monte Carlo t'vnits wcrr gcncralcd ovcr tlic wluitc Ql ränge rovcrcd In lliis iiicasiircinriitnaniclv fioni Q*nm = m*y2/(l - i/) to Q^ = -l Gr\'2 and in \\\ froni III Gi-V to l K) GcV,cxccpt for 7- and double dissociativc liackRtunnd evcnts, wliicli covrr a Iriggrr II'.,,, n'ginn(«10 G i; V < H\ < 300 GcV) Elast Je and prolon diswirialivi- pn cvnils wert- gcncnilcd in thcinvariant mass A/,*w- ränge 2/U, < M,<„- < 1.3 GcV.
In tlic following the tliroc Monte Carlo grncralors will be sliortly inlrodured Neu her gcner-ator siimilntes radiatiun oF real photons from tlic inroining nr onlgoing clerlnm, tior vacoiitnpolari/ation loops in thc virtnnl photon. Tlieir clfi-ct on thccruss scftion wns cstiinatcd to Ijcsnijillcr than 2% |GC] and thcir clfi'tt cm tlic slinpe of !hc M,tw ,\t\d angnlar dislrilnilionsarc expccti'd to lic ncgligible.
[>rot-(.-ss
rp-rp-rjt-
rp-<•;>-r/i-
•*rp/.a4rA r /»°4 r /fcj•+ r prf>* cp.\+ r /VA"
Monte C'arlu gcncratoiEPSOFT, DIPSIPVTHIA,EPSOFTPYTHI-VPVTIIIAPYTHIA, EPSOFTPYTHIA
Taldr "» 1: Thc Monte Carlo gcneralois nsed for thc diireicnl
Cli.ipli ' i 5. A l ' i r i f r ( V i r / n .S 'niml.i l i i ir i
5.1 DIPSI
Tlic Monte Carlo gcncrator DIPSI [8] is a gencrator for elaslic vector mcson prodnclinn. Itis liascd "n a tJC'D Icading log;iritliin modcl ra lcnla t ion by Ryskin . Tlic modc] assiinics t h a tt l i c cxchangrd v i r t na l photon flmlnates in lo a qq pair which t l irn intcracts wi th ;i glnonladder rmitU'd by die im-idnil prolon. Tlic Parameters of t l i c modcl arc tl ic stiong conplingconslnnt «s-, tlic hvo-ghion forin factor of tlic proton and thc gluon monicntiim densily inthc proto» jfl(.f.fl2) (f = (iV? + (/ + /V-)/"'1. ? = (A/? + g» + P/J/4). Tlic modcl tanbc nscd at tlic small valiies of q1 involved in pn pliotoproduction, if thc parametcri/ation forft)(r,<f) is rhoscn to rcprodncc thc cxpcrinicnlat da la . In this region of small q7 howcvcr itis donblful whcther thc fimction !<}(?,q1) cati still bc. intcrpretcd äs tlic glnon momciitmndcnsity in Mir protun.
For thc cvrnts used in this analysis thc cffccl ive \\\ dopcndcnce of thr cross scctinn was ofthc type H'°_2, tlic ( dependcncc iv;is approximatcly exponcnlial with a slopr of 9.5 GcV~2.Thc invariant niass A / » » » - was gpiirrnlcd äs to rcprorlucc, aflcr rcconstruclion, thc mcasurcddis t r ibu t ion . Thc dccay aiigidnr dis t r ibnt ion of thp dcray pions was gcncratcd according to5-channr! hclicity conscrvation.
In this analysis PIPSI was »scd äs a cross check of tlu- rcsults obtait ird wi th EPSOFT andfor thc calciilatioii of thc acccptancr of thc LPS (scction 7.4).
5.2 PYTHIA
Thc Monte Carlo gcncratur PYTHIA [98, 99| si innlatrs 7p intcnictions hascd on VDM andRrggc thcory (section 3.3.1 and srction 3..1.2). Thc Q* and y spcclra arc gcncratcd nstngIhr ALLM pnramctcriziition [3] of thc cp cross scctinn. Thc ALLM paramctcrization rrlicson a Ri'ggc type rclation similar to cqnation (3.12) w i t h Pomcron and Rcggcon intcrccptsthat dcpend on Q2. It was fit t cd to a largc nnnibcr of photoproduction and DIS datn andpro v i des a snioolh transition bctwrcn thc (wo kineniatical rcgions.
Elastic ii} and (J photoproHuction rvcnls wcrc gcneralcd acrording to an rxpnnent ia l ( dis-t r i bu t i on and 5-rhamicl hclicity conservation Thc slopcs of thc ( dislributions arc thoserncasnrcd at ZEUS [111, 112).
PYTI I IA was also uscd to study singlc (proton and plmton) and double dissociativc phoio-proditct ion. Thc dissociativo cross scctions arc givcn by:
(5.1)
(3.2)
whcrc llic stopc dccrcascs willi thc niass likc bsn = 2b 4 2f>i. In U'^/A/2 Thc rffcct ivepxponcntial slopc of Ihc ( distribntion is 5.0 GcV~7 for proton dissocinlion, G.8 Gr\"2 for 7dissociation and 2-2 GcV'~J for double dissonatinn Thc spcclniiii of d i l f t a c t i v c masscs Mis inkcn to bcgrn "2M„ ;ihovc thc niass of thc rcspcctivc incoming p a r t k l e (c g. 'IM, + Mp
for >)i -i r/V/)° ar,d 2A/„ + Mp« for cf> -* rj>.\) and cxlcnds to v/fr l U'>IP Thc fartoi-s /-\,,and F,,,) arc introilnccd in llic Rcggp f c r n n i l a lo supprrfw prodnrt ion close to l l ic k i r i c n i a t r c
l im i l and to g i \ an cnhaiiccnicnl of l l i c l<nv mass rcgimi, whrif ;i rcsinianrc s t i n c t n r c isobsi'ivcd in thc d a l a . So Ihc rcsonancc s tn i c ln re is moddcd dy an avcraging proccdtuc. Thcparinncters in llic faclors arc obtaincd froin » f i l (o /»/i//'/"1 data jf>8|.
I.iglrt dissocialivc Systems with masscs M Icss t h a r i l f!c\ abovc llic niass of l l ic incomingpartkle n rc simnlated lodiray isotropically int o a twohody slalc For morc inassivcdisso(.-ia-t ivc 1 systcnis Ihe hadroi i i /a l ion processcs arc s inni lalcd arcorfling to llic s t r r n g hadioni/ationmodcl äs inipIcmciHed in .1ETSET [98]
5.3 EPSOFT
Simi lar to PYTHIA thc. gcncrator EPSOFT |C2] s ini i ihi tcs 7/' i i i tcnich-nis bjiscd nn VDMand Rcggo tlicory. Thc EPSOFT program \\';is dcvclojtcil w i t h i n thc fnnncwork of HERWIG[74] and was tuncd to rcprodiifc thc propcilirs of phiHdprodnct iun collisions ohscrvrd inIhc ZEUS dctrctor [C2|. Likc in PYTIIIA, thc k im-mal i r s of t In- clcctron vcrü-x in tlic cpintcract ions was gnieralcd accorrling to thc A L L M para i r i cUTi /a l ion .
EPSOFT was nscd lo gcncratc singlc (proton and plmton) dissociativc f i n d r - lnMic /)" pho-toprodnctioii- Thc lal tcr wi l l In- disnisscd in dctai l liclow
Photon dissociation (77* -t .Y;;) is gcncratcd froin Ihc f i i l h m i n g f u r i n n t n :
wlirrc llic tonst a n t 0=(M l givcs Ihc r a t i o bclwccn t l i c s inglc d issocia t ivc cross scrtion andthc total one. Thc Pomeron intcrtcpt is clioscn lo bc <i|.(0) — l . l and i h i 1 cHiTl ive slopeis sei to bc byn — fi.l) GcV~2 . Thc dissocialr've nniss / l / \s gcncratcd bclwccn iUt + 2/U„,whcrc fi i\s thc niass of thc vector nicsons (M^> in 80% and <VU, .U,, in K) % of t he cvcnts)and Mv the pion rnass, and x/lTl Il'-,„.
Thc proton dissociativc cross scction is calcnlaled in r r l a l ion lo Ihc ela.stk rcaction:
~}t °j-m...J/^ *• (5-' ')
The sccond trnn defincs thc ratio of prohabililies l l ia l Ihr protnn dissociah-s in l» thc nnctc-onic system N to ihat in which it cmcrgcs i n t a c t . ll is dcrrvcd froin a paramclcr i /a l ion ofPP -4 PP and /'/' —* 1>N cross scctions (62). Thc rnu Icnnir rnass MK is gcneialcd in thc ränge(1.23GcV)2 < Mf; < 0.l 11' . The l distribntion follows an cxponenlial and was gcncratedwi th an cfTcctivc slopc nf "i.O Gt-V~ 2
Thc tiadroni/ation of the hadronie systcnis A' and N is simnlalcd nsing an a lgor i thm sim-ilar to that iisetl in HERWIG Thc pailiclc innltiplicilics atnl tlie inoiiient;i of llic hadronsIransvcrsc to Ihe pholun-Pomcrnn collision axis are simnlated nsing paramclcri/ations ofexis l ing dala, whitc the Inngi tudinal momenla are grticrated imiformly in phasc spare. Thisalgor i lhm was t mied lo ZEUS data nsing mm dif f rac t ivr cvcnts [02) In singlc dissodalivcevcnts, instcad of gcnerat ing thc 7p collision al an cnergv \\\, a coltision of the pholon (orproton) with ihr Porncron at an encrgv M\r MK) is s i m n l f i t n l ,
EPSOFT was nsrd (u ratni latr (he acceplani'e ctirrccl ions for c las l ic /»" pliniripnxbiclion.Thc Monte Carlo elh'ricncirs arc rel ial i le only, if thc gcncra to r dcsrr ilics l l ic physifs of llic
pmci'ss tindcr stmly corrcctly. The variables Q7, II*1in l, A/,».- and llir tlcray anglcs inthc hclicity systrin cos0h, <£,, and <I> arc nsrd In dcscribc p° pholoprodurtion. Sinrc thc
ontgoing clectron is not mcasurcd in tliis analysis Q"1 and <t> tan not |jr mcnsiirrd. Thcgenerated y! distrilmtion was rcwcightcd arcording to rqiiation (3.53), whcre the paranieter(! is dctermincd, linder tlic asFiimption of s-channcl lu'lirity conscrvation, front tlic pa spin
drnsity inatrix elcmcnt rjjg (3.71) by
l
((}2) is the a\cragi- (f of thc dala, assiiming thc Q7 dcprndcnrc givcn by cqnation (3.53).
Tlic avcragc QJ dcpcnds 011 thc maximal QJ accessiblc by the mcasnrcmcnl, Q^,aT andon f.7. The (J depcndenrc of (QJ) was approximatcd by a linear functiun according to(Q2) = (}t + Qi£3. Inscrting this rqiiation into (5.5) violds:
cJ _Q, («) + W i -
(5-6)
Q\d Q? arc dcterniincd and paramcterizcrl äs a fnnction o\Q^mai. So for a given Qj„ttt thc
viilurs Q] and ^3 aro dctrrmined and inserted in cqnation (5.R). Thc valncs for (() and (6)arc given by (3.(50) and (3.G7). £2 ti> be itsed for thc Q"1 reweighting is thiis given in tcrmsof r^. Thc optimal value ofrSJ = 0.01.1, äs deterniincd below, yields f,7 — 0.2.
Since «I1 can not bc nieasured, thc decay angnlar distribntion was rewcightcd according tocqnalion (.1.69), whcrc thc spin dcnsily matrix clctnents r^, rfl, and 5?r°„ arc discnsscdbclow and all otlicr .spin dcnsity matrix clcmcnts arc rhoscn arcording to s-cliamicl hclicity<'(iiiscrvalion and linder thc assntnption of tmhinil parity exehangc. All cleiiicnts arc ZITO,
cxccpt, r |_, = -3r?_, = 1/2(1 - r") aml Sr?„ - -»rfo = 0 |GO).
Tn improvc (hc agrcement botwcen flala and Monte Carlo in the rcconstrurtcd H'1P, PT3,
A/„ •,- and dccay angnlar distribiitions, the Monte Carlo was reweighled in an iterativepioeednrc. The rcconslriicted data dislribntions are comparcd to ihr rctonstruetcd MonteCarlo distributionsartcrstatistical snbtraction of the proton dissotiativc backgronnd (scctinn71) and after rewcighting for tlic calorimcter triggcr clficicncy (srction G.l.I). As the firststcp of this procednrc, thc acccptance corrcctions wcrc calcnlated using thc Monte Carlo
Parameter
MSr0»i
roo
-.0*M-i
nb
f
optimal value
771 McV138 McV
G. (188 G3 GeV-3
0.010-0.008
1 1711.34 GcV-s
3.98 GrV-4
ränge corrcsponding to oncStandard dcviation
G.1G8.01 GeV-2
0.0200014-0.014
1.2311.63 GeV-2
4.22 GrV-4
6.009.25 GeV~!
O.OOG
O.OOG-O.OT2
1.1111 4GGrV-'3.74 GeV'-4
Talilc 5.2: Thc final rewcighting Parameters and the ctiangc rorresponding lo onc Standarddcviatiun.
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ovcnts rcwoiglitcd to thc distribnüons äs nifasurcd with tlic ZEL'S 199."5 Hata |l 111]
Sin«1 tlic (P niass shapo is skcwcd and siinc lliis skcwing tliangrs \v]\\i t, ttir rorrrctctlM,+,- distribntion was filtrd in t bins by thc Ross Stndolsky paranictcri/alinn (9 Kl). In
tliis inodcl tlic skcwing is dcscribcd by a skcwing facttir (M,<,-/M,,«)"• Tlic paraincli-r n istrtatcd äs a frcc pnrnnictcr, whidi dqicnds on l. Using a linear fnncti'ni (n(|/|) = HI - »2!'!)tlic paramctcr »i and >ij dcsi-ribi- tlic f>a sliapc äs a fiinrtion cif I. Siniilaily t r » ihr /»" sliapetlic spin dcnsily matrix rlcmcnts rjj}, i-"l, and S?i'" arc dclermincd fmni a lil «f (3.72) t"
the rorrcctcd two dinu-nsional ci)sÖhl 0h distribnlion.
Thc gcnuratcd t distribnlinii is paraniclcri/<'d by an cxponcntia) (~ c*'+'( ) and thc grncratcdH'w dtstribution by a powcr likc (Irpcndcncc (~ ^"•,"],")- Tlio parainctcrs /*, r and n arcdctcrmincd a-s folloivs. Thc diffcrc'iicc of llic reniiistrnctcrl P^ valncs (f{ir thc paramctcr h
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Chapter 6
The Acceptance
Thc arcrpliintr of rliislic p° pholiipiodw t ion cvrnls is gnr t i l > \' arrrplanrc of Ml«' Hast k1
p IrigRrr and Mit- cHii'ii-nry of dir wirrt ion nits. Für ihr rf f i r i i - i i rv calrnlat ion of ih r scliT-t l i m ciits Monte Carlo nu'llmds ;irc uscil (scctiim 0.2). The tnr lhoi l usc.l to c lHr rmi i i c ihriicceptani'c of tlir p triggrr uscs Ihc (tata arid wil l In - cxpl-iincd in ihr ncxt si-rlion.
6.1 Trigger Acceptance
As nlrnidy (Irsrrilu'rl in chaplcr -t (lu- fh-ilicatrd /i Higgrr is nsiiig i n fu r ina t i rn i of thi- Inurkin^fliamlxT and Ihc calorimclcr a( t h c dilfcrciil (rigßrr Icvcls. Sincc llic srlrctioii rtils oti t l i fIracks for rlnstic />n t-vciits arc ÜRlitcr lh;m thc Ir igRi-r rnts liasrd oti Inirkmg, t l ic cllicirticyof t l icsfcuts is vcry high and wi-tl s i innlnlrd liy t l i c ZFl'S drlcrtor Montr Carlo S imula t ion .The rfficiniry of tlir rncrgv rrc|iiiri'iiu'ii( in tlir r l ivlrnnuiRncl i r srction nf ihr rcar calnriinc-icr at thc FI,T (7?^A/O,.7 > l(il Mr\') on ihr- olhrr hand is d i l f i c u l l lo dr icnninc from
5000-
4000
3000 r
2000i
1000 \+ E (GeV)
0.1; Monlc Carlo i -n t - igv spr< U um of " t h c n 4 f io in //' di-rays.
( Vr,-i;>(rl G. Tlic .I
llif drtcfloi Simulation alone. Tlic lypical encrgy of a dccay pion fmin a p° rleray (lignreG I) is dose (o the nuiniiuil Iriggrr Ihreshold of -101 MrV. Inartivc material in front of thecalnrinicter find ihr calüiration of tlir rncrgics in thc calorimctcr h'rst levcl triggcr CFLT(.scrlion 22.2) liavc a big inipnct on the triggcr acccptancr. Pions an- hadrons tml Ihrtrigger iises only Ihr cncrgy drposition in tlic clcctroiiiiignetic scction uf tlic calorimclcr sotlif dctails of thc intcraction of tlic Iow cni'rgctic piims wiih llir calorimcter arc inipurtant.These efFrcts must lir well nnderstood and simiilalrd to rdy on n Monte Carlo Simulationuf Ihr ZEUS dctrctor for thc acccptmicc dctrrminalioii- To rcducc thc uncfrtainty in thcmcasurcnii'nt coming from ihcsc etfccls a method to determine tlic REUfCpi.T triggcr acccp-lari'-c from data was dcvclopcil. This mcasiircd arrcptancc is uscd tu corrcct thc data forthr REMCn.i triggcr acci-ptancr.
6.1.1 Correcting for the CFLT Acceptance Using Data
A /»° dccays in n TT^TT" pair and llic signatnrc. of sucli cvcnts in thr ZEUS dctcctor arc twoüpposilcly cliargctl trncks in thc CTD and no cncrgy dcposilion in tlic CAL apart frcmi thrtracks So only thc pions can causc a triggcr If noiv onc of thc pions rauscs a triggcr intlic rcar calorimctcr tlic othcr piou cait ho nsccl äs an incloppiidctit tcst pion to nicasnrc ativliich niutiiciitiini tliis pion can triggcr an cvcnt ns wellFor tlic fi(TCptaii(T dctrrmiuation only cvcnts wliich fulh'll tlni rctpiircnicnts of an clastic /'"photoproilnction cvcnt arc uscd (chaptcr 4). Thc sclcttion ruts niakc snrc that also cvcntsarc acccptcd in tvtiicti only onc of thc dccay pions lins canscd a triggcr, in casc tho cnrrg_vin a singlc CFLT triggcr t »wer not matclico! to a trark is ttclow itfi JIPFO snpprcsxion of AMMc\'. In thc kincniattc ränge nndor sturly thc npriting angle of tlic t wo trncks is too bigto liavc both pions in thc samc CFLT Iriggcr towcr. So thc two pions can indcpfmtcritly
beampipe hole
excluded from the REMC Irigger
Figurc G.2. Thc fimr triggcr rcgiotis in F1CAL and a sdicmatic picturc of an p° claslicpliotuprodiiclinn rvcnts uscd for thc acccptamc cak-iilation Thc rirclcs aromnl thc iinp;iclpoints of tlir tracks on thr calorinictcr intlicatc tlic cncig>- ilr-|)i)sition of thc tivo pions.
o, 0.5u
2 0.4Q.OJ
S 0.3o
0.2
0.1
V
v 0.5u
5 0.4aa>ö 0.3o
0.2
0.1
00
50 100 150 200positive track
250 300 ""350* (deg)
* t
50 100 1~i"5Ö~' J 200 *"' 250negative track
300 " "" 350* (deg)
Figurc C.3: flEMCn i triggcr arn'ptancc Jis a functinn <>f ihr a/innillul angle 0,from tlic track hnpart point on ihr ralorimrlei, fnr piwilivr and negative tracks.
caiisc a triggcr. Sinrr thc C'FLT c.nrrg.v iiicasniciii''ni o['c;u'h ofilie fctur indepetidcnt iriggerrcgions in HCAI, is slored in thc ZF/US data strcain ffir c;nh evrnt, il is pnssiUr lo rrlatc aIrigger in onc of Ihr Iriggrr region to onr pion. This is dom- liy rxlnipolaling thr tracks tothc calorinielcr and llicrrby (Irtcriiiiiiing whirh triggrr rcpion is hit liy räch pion. For ihrtriggcr acccptaiirc detcrniinatioii cvcnts arr nscd in whirh ihc two pions liil nppositr triggcircgions. In thr 1991 dala sample ~ 20(101) events fnlfill lliis nnidilion. An evcnt of (histype is illnstialrd in lignrr 6.2. Thc positive pion hits diggi1! regimi fonr anil Ihr ncgalivcpion triggcr region six. If triggrr rrgion four rauscs a Irigger onr r;in nsc thc pion hitlingtriggcr region six a.s an indepcndcnt lest piun to rneasme Mir IriggiT arce])tanre. Sinre l.hecncrgy deposilion Ijclonging to a pion has a lateral spread and Ihr tiack extrapolation is noiprrfcct, for p.vents in whirh the scrond pion hils thc calorinirter closr to ;i hordrr betwcentwo triggcr rcgions (within 20 cm) also thr adjaccnt triggi-r region is irsrd hideeiile whclherthc sccond pion causes a trigger.
Thc REMCn,T Iriggrr actcplance is dcterinitird for positive and negative pioits separatdyThe aeceptanrc is nn;asiired äs a fimrtion nf thc pion mnnjentirm, ils a/innilhal angle uV(Irlerniined from the Irack impacl point on thc rr;n caloiimeicr, ;uid Mir dislarue /? of Ihr
impnct poiiit in (In- rcntrr of tlic IICHTII pipc Figure G.,1 slio\vs lliat tlirrc is no significaindcpcridcm-c iif tlic trigger acccptaiHc on c\o in t In- fürt her analysis the triggcr arceptantc isintegralen1 ovcr <f>. A st rotig decrcasc o f t he aerepliincc ean l»c scc'ii äs a fnnction of /? (figmcG t) Tliis tan b<- undcrstood from ihr kineniatirs of/>" pholoprodnclion. Tlic biggcr /? thcsmallcr tlir polar angle of the pinns and tlic smallrr tlic photon-proton ccnlcr of mass oniTgyM .,p. Small H'?(1 tncan small piun cncrgics and rcsnlt in a sinall thc triggrr acccplancc
II is ktnnv l hat ihr ntnuunt of inactlvo umtcrial in front on tht- raloriinotcr dcpcntis on thcpolar nnglf. Thrrcforc Ihr REMC-n.r t^igg1'' arrcpLnncc is incnsurcd in six rrgions in H,iniliciilcd in (ignr)- G.<1. Thi'sr rcgions arc dcfinrd lo takc Ihn niosl striking non-imifoiniilirsin inaclivc inalrrial distrilnition inlo account .
In fignrc G.5 thc triggcr acccptancc for negative and positive pions versus the particlc nio-mentuni is sliown The acccptancr rurve Starts at aroniu) 4*)0 McV and incrcascs slowly. Aplatcau of^ 0.5J to — 0.6 is reachrd above 1.5 GeV. The probability of a hadron showcr to
4l U. DO
§ 0.5O.
S 0.4u
°0.3
0.2
0.1
Q
-A
-
-
-
-
t
*
.
4
* *
, i
4t
* '
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,
t
*
, ,
1 t |+ l
t
,i n i i* , t M , i
* f 1 M|
. , i , , , i , , , i , , .t40 60 80 100 120 140 160 180 2C
positive trock R (cm)
v 0.6u
o 0.5aS 0.4u
°0.3
0.2
0.1
n
-. . • '
-
L :
r
, | j
*« *
, ,
* t « *
. , 1
4
* *
, ^_
M ' N *_i_j_i i ^
» ' V i 1 )* t * ii_I_^_ i. L . ^ _ , 1 . A*
negotive treck R (cm)
Figure fi.-|- The REMCf-n Uiggcr acn-ptamc äs a fiinctinn of thc distancc of tlu1 Irackinipatt point on the caloriincler and thc reutet of llic beani pipe /? for positive and negativetiacks. The daslicd vcrtical line indieatc ihr seveti hins whidi are nsctl in thc coriertionpioccclnre.
(iJ
o> 'ucB 0.8o.v8 0.6o
0.4
0.2
n
-
. +
. * « ** *
• • '
. •
* , - • . ' , . i1 2
negative trock3 4
P(GeV)
Figure G.ö: Tlic REMCn,t trigger airoptanrc äs a fiinctinn of tlir tiark iiioniriiliiin \P\rpositive and negative Iracks.
statt at a deptli x in thc calorimeter is approxiniiilfly give» by:
l
1.22A0
wherc. A„ is tlic intcnictkm lengtli. So thc prnbahility foi ihr liadronic slumvr nf onc offP detny pions to slart in the clectiomagnetic se<-tion of ftCAL is:
/0.9AU
- / P ( r ) r f j = l -Jo
Tliis niiinber is in ruiigh agrcenient will) l tu? probubility in figurc fi.j for nuiniriita aliovcthc irigger threshold. A not her oltscrviition is lli;it tlic slnpc for n~ is smallcr lli;in fnr n+ sothc proltaliility to triggcr an evcnt with a n~ is snialler tlian the probaliility fnr ;i n* of thesaiiie tiionicntimi. Tliis ran be tmnstatetl to the olvtenaliun tliat n" aml n1 nf ihr« sarnemunietit um dcposil diffcrcnl amounts of cnergy in thc ZF,US ralorirncli'r (rliapicr S.l).
Thc nicasnred iiuTplance rnr\cs arc nsed to rornvt tln- dal» for thc CFI.T iiiggei arcep-lancc.
6.1.2 The Acceptance Correction Method
As explarned in l!n' pic\s srctioii Tor tlic REMCn.t triggcr atceplancc dciermitialiiin sixbins in thc radial diMance /? an- nscd. For euch of tbese bins t l ic awptaiHT is measurcd äsa fmiction of thc inomcntum |P| separalely for positive and negative pions. Tlie mcasiircdaccrptances arc fittcd by:
Pj and P3 arc frec parainctcr in ihr fits. Tlic parameter P, is only varied insidc a givcn ränge.Tlic ränge is Hetcnnincd by fitting thc nicasured acccptanccs integratcd ovcr all li with aconstanl. Tliis fit is performcd in diffcrcnt rangcs and Uie upper and Iowcr bound represonttlic fhicüiations in the resnll öl" thc fit. Lini i t ing the allomxl valuc for P\s necessary, hccausoin thc bins of high /? thc statistics abovc- l GcV is vcry small and a fit of equation ( G . l )rcsnltsin nnreasonablc vahicsfor P\ Thc resultmg parameters from the fits of equation (6.1)für oll R bins arc shown in figurc 6.6 and tablc 6.1. The parameter P3 which is a mcasurc
0_0.7
0.65
0.6
0.55
0.5
0.45
o.«(
-
- -,
1
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)
If T ]&8t<MJ t-i
*-* 1i 1
. i . . . . i . . . . i .
—
50 100 150 2(
a>CJ.0.5
*£ 0.4
0.3
0.2
0.1
X, °«
.T. S t f •""' •"Tl T IwT- (jy&trr1
i
. . . . i . . . . i . . . . i . . . .3 50 100 150 2C
R (cm) R (cm)
u0.25-0.50.75
-11.25-1.5
-1.75-2
2.25-2.5(
• positive trackO negative track
-j-
^>-( 1 1E j i rV— i ,
K ..IM H-L- , ,_, i— ., iLJ , • ^ 1 1- t L 1MM _!_ -1- r i
H H |
j
: . . i . . i i , 1 . . . l L . . 1 . . . L . . . l . i i I j
) 20 40 60 80 1 00 1 20 1 40 1 60 1 80 2CR (cm)
Fignrc G.G: Parameters P,, PI and Pj of thc fits aerording to cquaLiciii ( G . l ) in ft bin Fnllciiclcs show thr rcsnlt for positive traeks and open tirclcs for negative trarks Thc vcr l ica lcrror bars n-prcscnt thc stat istkal crror of tlic fit and thc horizontal crror bai iml icales l l i csi/e of ihc R bin.
/? bin (ein)
30- 1 040-50
511-6565-85
83-10»100-130130-200
p;""r
0.08 i 0.1)3061 ± 0.04IJ.GI i 0.020.57 ± 0.1)30.61 i- 0.030.57 ± 0.010.57 ± 0.01
rr
0.60 ± IJ.Oj(I.GO ± (1.01
O.GO ± 0.0t
0.60 ± D.01
0 60 ± O.OJ
0.60 ± 0.1)5
0.51 ± 0-05
pf" (GcV)032 ± 0.0!)0.26 i 0.080 18 i' 0.10
0 IS_ t O.OG
0.2» ± O.O.')
o.:n ± O.IMo.36 ± 0.0:1
PJ"" (Gi-V)
0.17 i (UM0.27 i ».1*70.29 ± 0.01028 ± 0.010.21 ± 0.070.33 ± 0 .030.36 ± 0.03
/? bin (cm)
30-10•10-5050-6565-8ö85-100100-130130-200
P>3"" (GcV-1}
-1.82 ± O.r.l-2.00 ± 0 42-1.62 ± 0.40-1.57 ± 032-1.79 ± O.-IJ-1.56 ± 0.2!)-1.83 ± 0.38
rrMGi-v-1)
-1.58 ± U. 27-|.(KI i 0.26-1.52 ± 0.20-1.32 i 0.15-1.02 ±- 0.2-1-1 15 ± 0.23- 1 20 ± 0.24
Tablc 6.1: Parameters Pi, P^ and P3 of the fits ;K -rordi i iR t u cfinThc rcsults iirc given separately for positive J ind i i rg j i t i v r inicks.
m ( 6 1 ) for the li biiis.
of the tu rn on point of the trigger and the [uinimetcr P\s not slimv a dcpcndcncc nnthe cliargc. Thc parameter Pj describing tlie slop*' on thc mTi-pinm-c is bißgcr in all /? binsfor negative pions and some dcpcndcnce on /? c;ui tu - scen äs wrt l , rellcrling thc dilfcrentamounts of itiaclivo malcriai in front of thc r a lor i rnein
To corrcct thr dala for the triggcT acceptiincc all evrnis ;irc rcvvcigli lcfl . Thc rewi ' j g l t l i r i gfactor for each cvt-nt is thc invcrsc of Ihe Miggrr jn- r r -p tanci ' fni t l i is cvr- i i t . Taking theprobability t h a t bot h pions trigger an evcnt into amnint , t l ic wcight M',,, is givcn by:
»w, -irri, = 0 for ((|P|), -
(ß.2)
(0.3)
For f(|P|)„. and '(|P|)„- Ihe rrsults of llic lils an1 nscd To avoid big wciglits a cnt on |P|is introdtiLTit. So thp calcnlation of the CFLT ac<-i'ptam c fMiisisls of the fulknving sh-jw;
• cxtrapolalc llic tracks lo Ihe calorimclcr sntfiicc,
• caltiilat«1 thc acceptance f ( \ P \ for cnc-fi t rack. i f l h c t rat k hiis onc of thc HOAI, triggcrrcgions Tliis cnndition is fullilled if /? < 200 cm A Iowcr CM! on /? is not necrssarysiiKT a traek in thc CTD has a min imal polai angle which is big cnongh to hi t a l riggerrcgion
• srt r { \ P \ to /(TM if thc track i i iomei i l i im is bcloiv a givcn m i n i m a l n i n m e n t n m toavoid \-ery small valups of r rcsnlling in ver> big wciglits. The valuc fit i thc m i n i m a lmoiTieiitnrn is choscn lo bc 450 Me\'.
0.05
COS9h
Figurc 0.7: Thc mcasincd cos0h distribntion bcforc (du 11 cd tiistogrnni) and aftcr (fnll his-togiarn) corrccling for thc REMCpu- triggcr arceplance.
Tlir corrcrtion mi'tliod ran bechecked by applving it tosiiniilalrd p" events wliich are passcdtlirotigli tlie ZEUS dctcrtor simiilatiun. Calcnlating thc corrcction functions ((\P\) by usingMir Monte Carlo, Ihc prcvioiisly dcscribcd method reprodnccs vcry well ihr REMCn,i triggerarccptancc pul in thc Monte Carlo.
As iin cxample for thc corrrction proccdure figurc G. 7 slunvs tlic mcasiired cosflj, rlistribution,thc liclicity angle drfirird in srctinn 3.3.-l bcforc and aflcr applying tlic corrrction incthod.Thr dislribntion is asymmctric with rcsprct to zcro beforc t IIP correction. After corrcctingfur t In- R EMC FIT 'riggcr ac.ccptancc, Ihr distribulioii is Symmetrie Tho asymmctry can beundrrstood froni tlic fact thfit positive and negative pions of thr sainc niomrntiim dcpositdilfcrcnt animmt of ciicigy in tlic caloiinictrr and (lu-rcforr it is niurc liki-ly tn triggcr a p°cvnit by a positive pion. Tlir deciiy angular distrilmtion is discusscxl in inorcdctail in soction9. G.To (Irterniinc the cfficiency l'f the claslic p triggcr Monle Carlo, cvcnts siinulating plasticpn pliüloproiliictioii are iiscd These cvcnts arc passet! throitgh tlic ZEUS dctcctor Simu-lation program MOZART, thc triggcr Simulation prograni ZGANA and the rrconstnictionpmgratn ZEPHYR. Tlic cfiic'inicy of all trigger cnts c.xccpl the REMCtlil rcquirrment isilelrrniincd froni thc Mnntc Carlo Simulation, As cxplaincd tlic efficicncy of thc KEMCn/icul is corrcctcd by rcwcightiiig tlic dala and for Ihc Monte Carlo cvcnts thc sanic stcps äsfur 'lala arc applied but tlic cvcnt \veight II'"r*f,( (cquatioii (0.2)) is sei to onc.
6.2 Efficiency of the Selection Cuts
As alrcady describcd in chaplcr A thc following cnls are nsed to sek'irt clastic />" plmtopro-dnction evrnls:
• rims insidc thc selectinl run rangi'S,
• cxactly twy trncks of oppusitc cluirgc form a conunon vc t t i 'X ,
(17
• Ihc evetit vcitcs luis to lie ivitliin tli ITC Standard i|r\iatiinis of ihr nirjin \r t es pusitiun.
• tlu1 encrg\ of ihe most rm-rgclii- crll not iissignrd to tlic li;ick.- luis In br rmisistentwith noise in the calnhinclcr,
• (Hinlity ctits on thc irarks, iiatncly |//| < '2.1, P, > ITilJ MrV for c;uh trark.
• invariant mass as-siiniing ihe tracks are pions ,U„.„ < l.2 OV,
• si|iiarcd nioiiieiiliiin of thc- pn P] < U ö CJf\',
• invariant mass assnming thc tracks aie kaons A/h i h - > 1.038 UeV.
The cffk-iency of all thcsc cuts is detcrmined nsing Monte Carlo cvcnts. Events sirniilat-ing clastic p° pliotuiirodnction are passed tlirongh ihr ZEL'S detcetoi simnlalioti progr.iiiiMOZART, the Iriggcr siinnliition program ZGANA and thc s;ime rcroiistriiclion prograniZEPHYR äs tlic data. By thc nsc of tlie Monte Carlo evcnts llic arceptanrr for elaslic /i°evcnts äs well äs tht1 smearing in tlic kincmatic variables jux* ex'alnated. Thr acccptancc in-clii'lcs thc cllidetiry of the triggcr fuls, cxeept tlic HEMCn.i reiinirenicnl, and tlic rlfirinicyof the selcction cnts. In figurc G 8 and G.9 <s, defincd äs tlic Hinüber of events triggcred andsclcctcd in tlic gencrated variables uvcr thc gcncraled events is shown äs a fimrtirm of tlic p"mass, tlic plioton-proton ccnter of nias.'i energy U'7p, the transverse niotnciitiim sqnaie Fj oftlie p°, fit, und «wflft tlic liclicity anglcs delincd in seclion ,1.3.'). The statistical enoi slio\vnin ihe plols was calciilaled by error propagation froni thc stiilistinil crmr 011 tlic nninbcr ofgenerate<l cvcnts and tlic statistic.al crror on thc ntnnber of liiggered anil selerlcd cvcnts.The Monte Carlo program EPSOFT is nsc-il for thc sitnnlalion of tlie pioeess 7;; —* p"j>Thc acccplance incrciises for incrcasing M„>, and rradirp a platcan anmnd 8IHI McV. Thisacceptancc deercasc at sniall niasscs is dm- to tlie fact llial for sniall M*t,- thc polai jitinlc
0.5
0.4 :
0.3 -
0.2
0.1
* + * t* * * * * » »
* *t t
n C-L-. .. i . . i . - i . . . . i^.... t . . . , . _ ! . . . . . i , .... i . . . . i .-^...u,.,.0.2 0.3 0.4 0.5 0.6 0.7 0,8 0.9 1 1,1 1.2
M.„. (GeV)
Fig'ire 6.8: Acccptancc of the triggcr and Ihc selertion <-nts for elaslii' />° ptmlopnidtirliitnevenls äs a function of thc Mf>,
(IS f'. '/Tu
- 0.6W
0.5
0.4
0.3
0.2
0.1
n
r/\•i
*•• \
*,• : . , , i . , , . i . , , . i i . . .*.*
r 0.4*o
0.35
0-3
0.25
0.2
0.15
0.1
0.05n
50 60 70 80 90 100W„ (GeV)
• U.-l
0.450.4
0.350.3
0.250.2
0.150.1
0.05n
-+*•*•**: *•*•+!
- i+ \ + *
- * «-• * *--• •L . . . . i . . . . .
0,1 0.2 0.3 0.4 0.5P? (GeV')
cosft,
» U. -J
0.450-4
0.350.3
0.250.2
0.150.1
0.05n°C
- » ' » » A+ i +-* * t +- + »'--
. i . . . i . . . i) 2 4 6
*„ (rod)
Figurc fi.9: Acccptaiiec of the triggpr and tlic sclcdion cnts for clastic />" photuproductionevents äs functioti of thc kincmatic variables.
of t l i< - dccay pions is big so one of tlic pinns or evcn botb pions (for jU„.,- < 500 McV)don't cntrr thc CTD. Thc cut on iMK»K- «'ausps thc acccptance to bc vi-ry smatl bt'low 400MoV in A/,*,- , so the rcgion bclow 551) McV is cxcludcd Tor most of t l i c rcstilts prrscntc.din chaptor 9. As can bc secn in figure 6.9 tbe ninximum in the acccptance in \\\ is aroundCd GcV. For U'w sniallcr than 50 GeV thc cncrgy of the dccay pions is too sniall tu causca triggcr in ihc REMCf.-i.r and thc pions slart to h i t tlic barrel calorinieler DCAL. On tbedllicr band for big IV'1P tlic polar angle of thc dceay pions is too big to reconstrucl tlic pionsin thc t raeking chainbcrs Tlicrcforc thc analysis is limitcd lo thc ränge 50 < \\'-,p < 11)0GeV. Thc acccptancc is ahnost flat äs a Fnnctiun of Pf Im t shows a st um g dcpcndcnce oncos Oft and on <t>i,. For big valucs of |cosOh| and ^ ~- 0, TT or 2?r again onc of Ihc pions is out-side tbe CTD The kincmat ic variables arc corrclated. For cxainplc llic areeptancc is noarlyÜITO for small niassos and big |cosOft|. The Monte Carlo uscd lo caleulatc ihc arccptanceonly givcs a rcliable results, if ihc gcnrrator describcs thc niiderlying pln-sics weil To niakesiirc l l ia l tliis is thc casc llio ratio ofdata ovcr Monte Carlo has to bc Ihit in tlic nicasuredränge (seclion 5.3)
<>'->. Wticifitcy »f_(fif.SV/irti(iii
w0.5
0.4
0.3
0.2
0.1
%
f
~ + +/MI
~ *: * * * * * * ** T tr *: t
***
'_ • ••
•• J * 1 1 1 1 • l* I l 1 ' 1 1 l 1 - l I * r 1 , 1 l . , l 1 l l , . 1 l , . , 1 l l , , 1 , l l l
2 0.3 0,4 0.5 0.6 0.7 0.8 0-9 1 1.1 1 2M.„. (GeV)
Fignrc G. 10: Acceplaiicc (, whidi inclwles llic snicaring cortoclions äs ;\t inass M, t,-.m nf thc
The snicaring in ihc kinrmatic variables was alroady discnssed in wctinn (.2 Thcrc arctwo mclhods to takc tlic finite rrsulntinn in thc corrccl.ion prorednrc r n t n acnwnl. Tlu' firstone is to correct t h r mcasuml d i s l r i l i n l ions by f ? a r id f i t thc tom-ctcd disnibnt ions willi acomoliition of tlic rcsolntion l'nnclion fi ;ind Ihc fnnction dcscribing tl»1 [iliysics F So (In-fitnction uscd in sucli a H t rcads likc:
This integral can only bc solvcd in gcnrral for spcciitl cascs of tlic f m i r l i n n s /? and F. Tbccorn-ction proccdurc ustng tlit- tonvoliitrd fnnrtion / is applird in tlic stmly nf ihr invaiianlinass distributions (scction 9.3), wbcn- tlic convnliition integral is soh'crl nniniTical ly
A sccond inctliod to takc tlic rcsululion inln accoitnt is l<» rcdrfinr tlic arccpt;tiire, by Üierat in of llic ntimhcr of triggcrrd nnd si-litclcd cvcnls in llic rt-aiiistmclfd variable uvcr Llicgcncratorl cvonts in tbc gcnoralcd variable, Tliis iK-wptnncc f inclndrs die cirret nf rventtosscs anrf rcsolntion. Tbc stiilistical crror »f r was again ealenlatcd l»y crnit itnipagatiunfroin tlic statistical rrror on tlie iniinber of generalefl events and ibe s la t j^ l ical nror onihc nuinbrr of triggcrcd and sclectcd evenls. Distr ibut ions ei ' irectefl w i t l i ( ran bc dinx'llyconiparcd to tlic pliysics cxpcctatinn F(r).
The second corrt-ction mutbrxl is »sed in niost eases in t l i i s analysis Figurr fi.KI slitnvs äs anexample ( for tlir invariant inass. In nmtrast to (iginc G.8 i slinws a dip anmin l thc pn niass.Tliis is duc to Ihr fact that it is i n inc l i k i - l y for an eveiit In n i iRia teont n f o f (he f,n peak llianto niigratc int» tlic peak. The s<'cond eoncution inethod is simpler 1ml lia.s disadvantages.If tbe Monlc Carlo Simulation givew a wronß resoliilion ii is d i l f ie id t t» 'lelerrnine t l ic ffFctrlon llic l inal result, whcrcas in thc lirsl mcdmd only ff has to bc ebnnged A spceial ense ofa wrotig rcsolntion can occnr wben llie Monte Carlo pr<i|;nitn s i innh i l i i iK the plusies process(in lliis cnse /)" pliotoprodurlion) is not deseriliing tlio nnr le r lv i t ig physics weil. To makcsiiri- l l i a l ttiis is not tbe casc l he iat io of data nvcr Monlc Car lo evenls in all reronsl muti-d
v;m;iHi's h;is li> In- (l.it. In tliis iinalysis tlic EPSOFT Monte Ciirlo evcnls are irwciglilednntil Ihr ratios of data and Monte Carlo arr Hat. In lliis way thc Mimte Carlo is (iiiii'il to
(In- diita.
Chapter 7
Backgrounds to the Elastic p(] Signal
In lliis cliaptrr difTcrent sonrrcs of backgixmnd wliidi contiibnlc to ihc elaslii1 p" signnl willbc stiidicd. ßackgrmind cvcnls originale from r;» intrnirlinns, from bt-aingas intcriictionsand cosinic c\rntR. Tlic contribntioti froin Ix'amgas intcraclions nnd cusiiiics to tlir i'lfistirp° signal turnt'd mit t o Ix1 ncgligililc. Tlic Iwckgrntind fiom clastir phutoiModiirliun of u and0 nu-soiis and 7 and double dissunativi' plintoprodiiction is sntall. ()n tlic «tllirr li;ind protondissociativr f>° pliotoprodiiction accnnnts Tor 20% of thc si-K-rtcil cvcnls and is subtractcd
statisttcnliy,
7.1 Proton and Electron Beamgas Background
Bramgasovrnts rannot br dislingnishrd from r/n-vcnls, if tlicv on-nr dose (o the interacti'ipipnint. Tlicrcforc thcy wcre snblrartcd slalistically nsing pilot Inuidics. Pitnl bundies arc
impfiired clrctron or proton bnndics, \vhcre tlie nF-bnrkct uf (he otlier ]>ailidc spccirs isnot filled. In 1994 HERA opcralcd typicalty \villi llie ri)ll<in'ing Inindi configiiration:
153 ck'ctron-proton htinclics (rp btm<:hes)
15 clc-ctron pilot bunches
17 proton pilot bnnclics
35 einpty bnndics
For llie statistioal siibtraclion, the sclected evenls wliidi originalrd fnun thc pilot bmiclieswen1 addcd to the data sample witli a nt'gsitivc wciglil. This ueighl is gi\Tti by tlic piobabilitylo gcl a bcanigas cvcnt \vliile lillcd ck-etron and prntnn bnndics rollidcd in ZF.IJS Sincc IhriiiittiniT of bcainga.s cvcnls is proportional l o tlic L'iirrcnl in llie corieKpnniliiig bnndics, l he
wciglit is givcn by llie tatio of thc ctirrrnt in all pilot bundies ovcr Ibc nirrenl nnitained inall colliding bnndirs for cadi particlc type:
lu, _ f,t in all cp bmiclies
r /,» in all r* pilot bnndics
ii'F-M 'f '" a" r'* bnndicsF /,, in all p pitol Iniiidics
7. linrk£tinitnlfi tt
Assiiniing t l i i1 siinic r* aml }i l ifctimcs of pilot and r;; hnnrhcs, thc wcights arc constantw i L l i i n onc l lC f lA f i l l . In lliis iin;ilysis llic wcights \wrc calmlatcd for oicli plivsics runsrpjirali'ly.
S imi la r ly Id bcimigas rvcnts, cosmif cvciits coultl )><• snbtraclcd froni ihr sample s lat is tkal tynsing llic cmptv hunclifs. In Ilie final sample 49 eveiits werc found in llic elcctron pilulImtulics, but luiiui i» llic proton pilol bunrhes. Tlic nictm wcights (ll'/*'"') = -10.2 and{n''"1"'} = -9-7 and an uppcr bound of l cvrnt in proton pilot bnnrtics rcsnltcd in a contri-Imt ion of O.G±Ü.1% clcdron and <0.01±0-01% proton bcamgas cvciits in the f inal sample.NH cvnil was found in cmpty bunrhcs. Tlic clcrtnin bcanigas contribntinti was snbtracti'dstat is t i tal ly in all turrcctcd Histributions in rliaptcr 9, whrrcas contribntion froni protonbcningas and cosmir cvciits wcrc ncgk-clfd.
7.2 Photoproduction of u; and 0 Mesons
In tlicsc procrssrs n ui or <i> inrson is proHurcd inslivut of a f>° nic.son in llio f ina l slatr, Tlicscbackgroiinrl rcactiuns wcri' slndicd using Monte Carlo cvcnls froni tlu1 PVTHIA gnicrator,whicli wcrc passcd tlirougti thr ZEUS rictcctor sinitihition program MOZART, thc triggrrsitnnlation prograni ZGANA and llic rcronstruction program ZEPHYfl. Thc niost iniportantdccav chamiL'ls of thcsc nicsons arc:
-» 7TT7T fl 77) BR: 87 7%
BR: 8.4%
0 -t A'*A" DR: 49.1%
<}> -t A~?A'£ DR: 34.3%
<jt -* p, -nrNr'jr0 BR: 12.9%
0 -» ff + ff-]T°H 77) BR: 2.5%
From llicsc dianncls only t hose whicli conld Icavc tlic sä nie signatiirc a.s thc p° —t 7t + 7r~in thc ZEUS dctcctor wort1 considcrrd. These wcrc thc dccay chaiincls w or if> -t jr*jr")i0,if thc cvcnls wcrc not rcjcclcd by llic cncrgy dcposition canscd by thc dccay of tlic TT°,and 0 -> K*K~ sincc im partiele idciitification was nscd in thc annlysis Sincc thc PI oft l ic vrctor mcson is vcry small, thc final statc pions in tlic 0 dccay chnnncl A'JA'* cscapcniKlctectcil tlirongh thc bcampipc, so this channcl docs not eontributo to tlic p° Signal.Dccays of thc 0 mcson in Iwo kaons wcrc idcntificd casily, sincc thc mass difFcrcncc betwi-cnthc 0 and llic t wo kaons is vcry small As a rcsult llicsc cvcnls shmv np in llic invar iant nmss(l is t r i l )u t ion clusc to thrcshold. IndccH in figurc 4 .11 a small pcak is scc" at /Uw*,- < 400McV. This background was tlms rcjcclrd complctcly by a cut on thc invarianl mass ofM* >h- > l 038 GeV, calculatcd from thc track morncnta assnniing kaon mass.
Figurc 7.1 sliows the invariant massdistriliulion frf,t,- aflcr all p" sclcction cuts for w (uppcrplol) and 0 {lowpr plot) nicsons dccaying in thrcc pions. u cvcnls pcak weil bclow thc p®pcak, whcreas 0 nicsons show up nndcr thc /> rcsonancc äs well. This can bp cxplaincd fromllic fad tliat 0 inpsons can dccay via thr chain <j> -t p°x° ir~ii0. Using Ihc mcasurcdrniss scctions of clastic 0 and uj photoprodnction ( 1 1 1 , 112] and tho branching ralios (82)thc fol lowing ccintrüint ions wcrc dclcrniincd:
T.2- / ' l iutu/ irctfnctf tw
VI
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«. (GeV)
900800700600500400300200100.
l .M T . l 1_1_J ! !_, ._-_!_] .-L-L-Lj., !_ l U _L_L_ , L I Ü *_! L l ,1.1 J..I.I ,
0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1,2
M„+„_ (GeV)
Figurc 7.1: Invarianl. imiss d i s l r ibn t ion iW r . , - fnr u1 (nppcr plol) and </> {Iowcr plol) nicsonsin thc thrcc pion dccay modc froni a Monte C'arlo S imula t ion , a f l c r all pn sclei tion culs.
• background contribii l ion froni u-' -> 7r + 7i~n0: 1.2±() 1%
• backgronnd conlribntion froni <t> -» •n*-n~nn. ().4il).l%
Thc background from cliistic 0 pholopiodnclion is llni.s vcry .small and was ncglcclctl in tlirfurtl icr analysis. Thc background froni clastic u; pholoprodnrtiou wass i ib l ra r tc r l s ta t is l ical lyfroni all distr ibnüons. Most of ihr rcsults prcscnifd in chaplcr 9 wcrc dcrivcd in thc limitcdmass rcgion of l) 55 GeV < M,-w- < 1.2 GrV As can bc si-cn froni thr uppcr ptol of lignrc7.1 thc contribntion from w pliotopioduction in (his mass rcgion is vcry small {(} 1_t().l%)and li-ads only to a small slatislical snbtinction.
(7i,i/tfci t<> 1 1 H' Eln.it_H'_j>
7.3 Background from 7 and Double Dissociation
Photon dissociation and double dissocialion nrc dilfractivc procossos cif t hu type 7;> -t A'pand ->p -t A'A', whcre A" and /V arc slatcs of mass rt/,x and MK, which dccay into (inalstatc hadrons (scction 3.3.1). Double dissociative; events contritnitc to thc final elastic /i°signal, if the mass MN is sniall, so thc stale N cscapcs thc dctcctor undctrctcd througll thcforward brampipe On ihr othcr band thc dcciiy products of thc s täte A* have to fnlfili alltbc elastic p° srlrctiun cuts. T wo Monte Carlo progranis (PYTHIA and EPSOFT) wcrc uscdto studv tbr acccptancc of thc statc A'. Details on tbc Monte Carlo prograins and on tbcmass dislr ibution of A' and N uscd in tbc Simulation can bc found in chaptcr 5. Monte Carlocvcnts wcrc grncralcd in the H'7P ränge betwecn 40 GeV and thc kincmatic limit. Figurc7.2 sbows thc gcnrratrd W-,v distribution for 7 dissociative cvcnts which fulf i l l all clastic pa
srlection cuts. It is sccn (hat thc background from 7 dissocialion is mainly causcd by cvcntsfroni thc sanic H'7P ränge äs u.scd in thc analysis of elastic p° photoproduction, namely fromH'1P betwccn 50 and 100 GcV. Figurc 7.3 shows thc A/. t»- distribution up to 1-2 GcV forcvcnts gcncratcd by tbc two Monte Carlo gcncralors aftcr applying all elasüc p° sclectionctits. For thc cvcnts generatcd with PYHTIA (uppcr plot) an increasc of thc background forincrcasing mass is sccn- In contrast, for EPSOFT (Iowcr plot) thc 7 dissociative backgroundis flnt in thc A/».,- rcgion undcr study.
Tbc acccptancc for double dissociative cvcnts «'äs dctcrmined using cx-cnts gcncratcd withPYTHIA The- grncratcd mass distribution for ;U* Starts at A/,, + 2 A/, =s 1.2 GcV, Thc sbapcof tbr rcconstructcd A/»»,- distribution aftcr all clastic pn srlection cuts is vcry siruilar totlu- PYTHIA rcsult for 7 dissociation but tbc ovenill accrptance is two timcs sniallcr.
TIii- mnoiiiH of background from 7 and double dissnciatirm to thc clastic pQ signaf dcpcndsoti thc arccptanrc for tlicse proccsscs and on thc ratio of thc cross scctions cif 7 (or double)dissociative photoproduction to clastic p° photoproduclioii. Unfor tunatc ly thc acccptancc
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Fignrc 7 2 : Generatcd ccntcr of mass ciicrgy \\\„ for i dissociative Monte Carlo cvcnts, aftcrnll (P sclection cuts.
7..'). /t;irfcj-nnim/ 7 ,-ui'i (l)unliir
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0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1 . 1 1.2EPSOFT M„„_ (GeV)
Figurc 7.3: Invariant mass distribution /V,t,- for 7 dissocialtve cvcnts, aftcr all />" sclcrtioncuts, gcncrated by PYTHIA (uppcr plol) and EPSOFT (h wer plol}.
for 7 dissociative cvcnts difFcrcd betwccn thc two Monte Carlo gcncrators PYTHIA andEPSOFT by a factor of !.8%/0.3% = G. Also tbc ratio of thc 7 and double diwwiat ivr totbc clastic p° photoproduction cross section is not known. Dcpcnding 011 the assiiniplinnsmadc in tbc anatysis tbc valucs in table 7.1 were obtaincd at H'1P Ä; 200 GeV. So thebackgiound from tlicse two proccsses cnn not bc snblractcd easily. Instcad a liackgronndtcrm was includcd in thc fits to tbe corrccted mass i l t s t r i b i i t i f t n s to arcouut for 7 and doubledissociatiou. Tbc sbapc of tbc batkground was dclcnnincd from thc A/,. ,- distribulion foi
HlZEUS
assumption]-G3iO_890.8910.41
Tablc 7.1: Mcasuml ratios of 7 and double dissociativc iiliotopruduction cross sirt.iim (n, ,,,.,öjbrf,.) to llic rla-stit p" pliotoproductioii cross section at M'1P =s 200 C!cV [108, r>0|. The rrnirswcrc calculatcd from thc indiv idual cros.s scrtion errois frnin thc referencc.s.
(,' 11 afUcr 7 Uiifk gnmtiils lo llu* Eliistif /P Signal
thc PVT1IIA gcncrator (iippci plol of figurc 7.3) aftcr applying thc claslic pa acccptance inA/,,,- (figurc G.8):
.) = " » ( ! •"+ l..W, (.- |GrV)). (7.1)
In t he mass lils in chaptcr 9 this tcrm was addcd and .4 was a fr«1 paramctcr of tlir fits.Tlir filtrd valnc fur A corrcsponds tu iin inlegnilcd contribiition in tlic inass rangt1 0.55 lo1.2 GcV typically smallcr than \% of ihr tlir lotal.
7.4 Proton Dissociative pn Production
Thr most iniportant background to rlastic p° photoprodnction is prototi dissociativc p°photoproduction. In thusc cvcnts tlic outgoing nuctcon is a statc /V of mass MN which<lrcays into final slatc hadrons.
Thr contribution of this proccss, rp —» r^N, was dctcrmincd from data and clastic /i° MonteCarlo cvcnts, and not froni proton dissociativc Monte Carlo cvcnts. Proton dissocialion wassludicd using subsamplcs of dala cvents, which wcre taggcd äs proton dissocialive by anoncrgy dcposition in thc direction of tlic outgoing nndcon. All clastic p° sclcction cuts wcrcappliorl, cxcrpt tlip cut on thc oncrgy deposit in thc FCAL (spction 4.3.2). To havc a goodagreomcnt bplwee.n data and Monte Carlo for tlic FCAL BPn,T triggcr rpqnirrnient a cutim EFCAI.RII < 1-2 GcV was applied (scction 4.1). This rrrpiircmcnt limitcd thp acccptrdniiisscs Mfj brlow "- 10 GcV.Proton dissociativp cvrnts wcrc idcntificd by onc of the followingn'(|inri'rncnt:
• a PRT lag, a sign.il of at Icast l MIP in i-arli connttT of one pair of ronntcrs of tlu-PRT {scction 2.2.3). Thc acrcptancc of llic PRT lag in M N incrcascs towards vcrylow niasscs and drops fcr Uff, < 3 GcV. In 199-1 tlic PRT was opcrating only in pariof thc liiminusity ränge nscd in this anatysis.
• a FCAL tag, an rncrgy dcposition in thc two inncrinast rings snrronnding ihr bcanipipcof E n-A t. H ti > 0.4 GcV. Tlic acccptfinrc itf Ihis tag is const.int in thc mass ränge froni-3 ti> -10 GcV and drops to /cro bclow 3 GrV.
Fignre 7.4 shows thc ratio of PRT taggcd cvcnts ovcr all cvcnts fnlfiUing thc clastic p°sch'i'tion cuts, äs fiiiictioii of M,*,-, U'w, cosBh and P*- in thc PRT luininosity ränge. Tlicralios arc Rat in M,<w-, U'1P and thc dccay anglrs. Un<lpr the .issiimption, snpportcd byhotli EPSOFT and PYTHIA, that thc roquircincnl of aclivity in thc PRT docs not affectth<' shapc of thc arrcptancc äs funclion of Mw*,-, U'1P and thc dccay anglos, this resultiutliratcs lhat prolon dissocialive and clastic p° pioduclion havc the same dcpcndcnce onthcsc variables. On the othcr hand thp ratio increases äs a fnnction of P7J. Tims the l slopcsof clastic and proton dissociativc f>° photoprodncticm arc diffcrcnt, A similar bchavior ofthe ratios äs function of the kinninatic variables and thc dccay anglrs is smi for tlic FCALtaggcd cvcnts.Tlic P7? dcpcndcnce of the proton dissotiativc harlcgrontid tu thc clastic p° signul was dcter-niincd froni (tic ralio /?,., of tiigged proton dissociativc cvents (by thc PRT or FCAL) ovcrall cvcnls fuliilling the rlnstic p° selection cuts. Assnitiing an cxponrntial sh;i|ie in Pf forclastic (,4„.(•-'"•'r) and proton dissocialive (,4pd„r"*<•• '•• 'T) p* cvcnts fnlh'lling llic clastic (P
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Figitre 7.4: Thc ratio of PRT taggcd c\cnls (<} all cvcnts ftilh'lling llic rlastic />n sclcctioncuts äs function of dilfcrenl kincmatic variables. Tlic ralios an- flal, cxccpt Tor Pf2, whcrcthc rcsnlt of a ht with cqnation (7.2) is sliown Only stiitistioil crrors arc sliown.
sclcction cuts and Ihe same stopf in Pf for proton dissocialivc cvnits laggr-d in llic PRT orFCAL (61M) and sclcctcd by llic clustic p° st-lcction cuts ('j„,,,.), ihc ralio /?,., can bc wriltcnäs:
/?,.. =
(7.2)
The s<'cond asstimption ('),., = 6p,i„) is fulfillcd since taggcd cvniis ni\-rr Ihc |mv MN rcgion,which is thc inain backgrounil conlribntion tu the clastic signal äs well, and tlie acrrplanrcin Pf- has thc same shapc for Ihe PRT (or FCAL) tag seiet -Hon and Ihe claslic />" sclcctionTlic slopr bdl(f = t,,. - b„A.. is llie slope difference betwcen claslic and proton dissociativc p"pholuproducliiHi This paranicler is dctcriiiined by (iltinn c(|iiation (7.2) lo tlir tnca.snrcd
in4-1cV
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900800700600500400300200100
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Fignrc 7.5: The i,, d is t r ibut ion äs mcasnred by the LPS in thr 1994 ebstic p° sample. Aclear pcak al T/, ss l is scen, corrosponding to quasi clastically scatlrrcd protons. Only thcslatislical crrur is shown.
rnt io /?,., {Iowcr riglit plot o f f i g u r e 7.4).
= 4.79 ± 1 . 4 7 stm. ±0.52 Syst. GcV2 PRT lag
= 4.09 ± 1.96 st« ±3.12sjsi . GoV! FCAL tag
(7.3)
(7.4)
Tlii1 systematic error was delcrmincd froin thc higgcst chango in bdl» for dtfferetii fit ranges.
The absolute normal iza t ion of tlic proton dissociativc background contr ibntion was drtcr-iiiincd by a riK'asurPiiiL'iit \vhirb doos nol dopend on tlic simtihition of proton dissoriation.In 1994 Ihc Icading proton spcctromclcr LPS (scction 2.2.3) took data for thc first tinic.Tli«.- LPS nicasuros thc scattcrcd pruton. Only for a part of tlic 199-1 luininasity thc LPSwas iiiscrtrd into thc proton branipipr coinplptcly, so an clFrcüve (afli-r a proscale corrcc-tioii w i t l i c<|iiation (4.1)) intrgratrd luni innst ty with thc LPS of Cu>5 = 226 ± 3 nh~' wasiivailablc. Tlic LPS acccpts quasi clasticiilly scaltcrrd protons willi a transvcrso momcntums(]iian'<l r*p bctwccn —11.07 and —0.4 GcV!. F/ t-an bc usod to tncasurc tlic diffrrcnlialcross scction do/ttt for clastic p° pbotoproduction [114]. In tliis scction tlir LPS is usrd äs aIngginR dcvii:p for clastic p° cvcnts, but ihr P7J is calculiilcd fnun tlic p°. Fignrc 7.5 showstlir iiicasnrcd dis l r ibnt ion in Jf. , drh'iu'd äs thc ratio of thc incasurcd ]>roton nioiiicntum(i\cr llic monicntuin of thc inconiing prolon (820 GcV), aftt-r all clastic p" sclcction tnls andIho foltowing LPS sclcction cuts:
• onc LPS track in 2 or 3 stalions,
G o f ihr LPS track h t ,
• dosest distancc of thc LPS track lo n boani apcrtnrc > 0 •"» nun
On lop of t I IP LPS sclrctinn cuts, thc fdlliuvjng wciglil f;iclnrs lind tu !»• appl i i>d
/Ji-istu-j ' .itirc //' f ' j
A fiirtoi of 1.1 td takc ;i nin dopcnrlcnci' uf thc LPS pul posilinn in to ncinitnl Thc|)u( position in tlic Mond1 Carliyvas sei to ihr posiliun in um 9720. Tlic wcighl fnctnrtakcs llic run dcpcndcncc of thc LPS jicccptancc dm- to llic dilfcrcnt put piisitions in toaccoiint [9(l|. Tliis corrcction is indcpciidcnt of Ff- .
A factor of 0.95 to rorrrd for randotn coiiK'iilcnccs liclwccn a LPS Inick fnun a hiilopro tun and a p° cvcnt. Tliis farlor was dctcrni inrd frotn DIS c\-nits and tbc F. + Fx
cotistraint 90.
For clastic p" pholoprodnclion .r,, can bc wr i l tcn äs r,, = l - {QJ -f jU*„ f [ 'D/H'2 , , so forthc sample uscd in tliis analysis thc valuc of .r/, diffrrs fmm n n i t y by al niost 0.2%. In f i g i n c7.5 a clc.'ir pcak at i/, K \s sccn \vliich corrcsponrls to »|iiasi clastically scatlcrcd prolons.Thc mcthod to dctcrininc thc normal i/a t ion of (»roton diswicinlion is i l lus t rn lcd in f igurc7.G. The P/- distr ibntion äs niKasurcd by thc p° for all cvcnts \v i th in Ihr I,PR huniimsityränge ts shown äs a si;lid linc Thc dottod linc shows thc rvcnts wiih a protmi in thr LPS of1.02 > T,, > 0.98 and Ihc dnshcd l i t i f t h o s a m r cvcnts aft i -r LPS iKTcptJincc corrcction. ThcLPS acccptancc was rlclcrmiiird nsing thr avcragc of thc Moiilc Carlo progr;ims EPSOFTand DIPSI (e,.,.s äs 10% for 0.075 GcV2 < Ff < 0.5 GcV3). For P,2 < 0,070 GcV2 Ihc LPSacccplancc dofreascs rapidly, so t l i is ränge was not considcrrd in Ihc dct iTininat ion of thcproton difisociiitivc biu-kgronnd contr i lmtion. Thc amoiint of proton dissocialion is givcn bythc difforrncc hctwcen thc fnll and thc dasbcd linc, indicatcd in f ignrr 7. (i by thc i lark shadcdarca. Sin« thc statistics of LPS laggcd cvciils in thc 1991 d a t n is l i m t l c d thcsc c\-cnls wcrcjust uscxl to dctcrininc thc absolute normali /at ion of Ihc proton dissociati\ contribulion
W
V
10
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5Pj(GeV')
Fignrc 7.6: Thc F} dis lr ibi i l ion, äs nicastircd by tln' p°, for all cvcnls in thc LPS l i i n i i n o s i l yränge ( f u l l l inc), all cvcnts with a proton in thc LPS of 1.112 > r, > 0 !lg (dotlrd l i nc ) andIhc LPS acccptancc rorrcctcd dislribulion (tlashcd linc). The da rk slia<h'd arc;i indicalcs t l icamoiint of prolon dissociativc p° cvcnts. Thc vcrtical arnuvs indicalc thc ränge in T2 nscdl r > dctcnuinc thc absolute normali^al ion of proton dissorialivc backgroiind (0.1)70 < Ff <O ^ O Y 2 ) .
8l) 7. n.i'*j;i(nimK ki tl«' KJJV-IH- /•
tn thc das t k /i° signal in ihr P.f ränge bclwcn 0.075 GcV2 ;ui(t 0.5 GcV2. The PRT (»rFCAL) tagged cvcnts wcre nscd (<j nicasurc. tlic Pf dcpcndcncc of th is contribiit ion.
Fignrc 7.7shows tl ic ratio /?„,,.. of proton dissociat ivc events, givcn by 11»1 dirfcrcnce bctwccnall cvcnts ful l i l l i i ig thr ctaslic p" sdcclmti cnts and tlie acceptance corrcctcd events of 1.112 >T, > 0.98, ovcr all cvcnts fnllilling llic clastic p° sclection ciits for tltc LPS luniinosity rangt-.Assnining again an cxponential P* distribiition für clastic and pruton dissociative p" cvcnlsIhr ratio /?„,,,. is:
4- l(7.5)
A fit of cquation (7.5), with a fixcd slope (7.3) from PRT taggcd events yields for thcnorinalization factor N:
N = 7.34 + 1.16 . ,-0 M slflt-+ 1 3l ..-1.07 s>'5t-
±0.74 syst. fit + ,1* sysl. n.i-s. Q 27
weight pol ^0_25 syst. weighl halo (7.6)
whcrc N is tlic nican valuc of tlic rcsnlts dcrivcd for llic t wo Monte Carlo gcncrators iiscd fortlic LPS acceptancc corrcclion. Thc listod systcmatic crrors arc thc crrors duc to a changcof thr fit ränge, a systemnlic unccrtainty of thc LPS acceptancc of ±8% (±G% imccrtaintyon tlic aeccptance for a proton track in tlie LPS (l 1-1] and ±5% alignmcnt unccrtainty addcdin (niadrii lnrc), an unccrtainty of the pot posilion rcwc-ighting of ±57o and an unccrtaintyof lialo proton rcwcighting of ±1%.
0.05 0.1 0,15 0,2 0,25 0.3 0.35 0.4 0.45 0.5P? (GeV2)
Fignrc 7.7: Aeccptance corrcctrcl ratio of prolon dissocialivc cvcnts over alt events f idf i l l ingllic clastif p° selection culs, detcrniined by thc LPS äs a funclion of P\, The line sliowsthc result of a fit with cquation (75), willi a h'xcd slopr (7.3). Only thc statislical crror isshown.
.i. i'tnluit 81
To corrcct for thc proton dissociation baekgroiind cotilribii l ion all selc'clcd clastic (i evcnlsan1 weighted by:
. '/?.,. - l -/?P,,,. (7.7)
Rcweighting the Pf- d iRl r ibnlJon rcsnltcd in a con l r i bn t i nn of prottm dissocialion to tlicseleclcd olastic sample of:
(for Pf < 11.5 GcV2). (7.8)
A background contribulion of 20% is consistcnt ivilli ii calni lal ion of Holt mann et a1.|57].Thcy cstimatc the proton dissociativc backgronnd contribntion to clastic /7° photoproduclionto bc 0.20-0.22. Tlic ränge corrcsponds lo an nppcr l i r n i l on MN bclwi-pii 5 Gr\ anH G GcV.The valucs givcii in [Ö7j harl to hc corrprU'd for th'1 P? rnl tnking inlo atcoiinl tlio dilfrn'nt|f| slopcs for rlastic and prutun dissociativc pn prodnrtion.
Tho nirasurcnicnt of thc proton dissocintivc backgronml did not dcjiciict on aiiy prolondissociativt1 Monte Carlo gcncrator. No\ ihr data wil l l n- coniparcd to t In.1 l wo Monte Carloprogranis EPSOFT and PYTHIA. For proton diKSotialivi- cvrnts U»1 df-pi-iiririii-f on thcnnclronic rnass Ulf,-, in thr rogiun abovr thc rrsoiuuiccs (10 Gr\'3 < Jl/jJ, < 200 Gt'Vz), auibo dcscribcd by rf<r/r/fl/J oc 1/A/JJ- w i th an cffccltvt1 powrr n. A incasiirciiK-nt froin tlir CDFcollaboration in pp ~* pA" «t ~J$ ='800 GcV |19] yirlds ti = 2.21 ± 0.112 sint ± 0.02 B>st. .Thc powrr n for thc -yp ZEUS data can bf dctcrniincd froni l l ic p° plioloprodtirtion cvcntsby cornparing thc sltapr of thc cncigy d i s t r i lm t io i i in FCAL bftwccn 0.8 and 2.0 GcV. Anicasnrt' of thc shapc diffcrcncc hctwccti data and Monte Carlo is givcn by l l ic \ , rak'ulatcdfroni thc FCAL cncrgy spctlrii, normaliml in thc rcgion bcl\vccn 0. l ;ind 2.0 Gi-V:
|7.9)
In figtiro 7.8 \ is shown versus t tu* \ a lnc of n for tl ie gmcrator PVTHIA. Mininia in thcdistribntion wcrc found for tlie two gcncralors:
n = 2 .0±0 ,7s t a t . i O . ä n y s t .
n = 2.4 ± 0 , l s t a t . ±0 .1 syst.
PVTHIA
EPSOFT
The statr.stical crror is givcn by tl ic cliange in n for a cliangc iti \ by l nnil and tlicsystcmatic error is dne lo a changc in tlic fit ränge. Thc m i n i n i a arc vcry broad, becanscthc cncrgy ränge whicli coiild bc uscd is vcry small dnc to tlic t ight FCAL DPn.'t nil. ThcPosition of the mininia wcrc indcpcmlcnt uii thc / slopc; nscd in thc gcncration of llic MonteCarlo events. Thc ineasnrcmciit is cinisislcnl with Ihe CDF ineaMireiticnt.
Data and a mixhi rc of Monte Carlo cvcnts of 80% clastic aml 20% proton dissocialivcp° cvcnts aftcr applying all clastic pn sclcction ciits ( inclnding P-f < O.y GuV2) can bcconijiarcd to scc whetlicr the two prolon dissociativc Monte Carlo gcncrators EPSOFT andPYTHIA arc ablc to dcscribe tlie d f i t a . These two gencrator are frci]iienlty nscd in the ZEUScollaboration to dctcrniinc llic prolon dissoci;uive backgtoutid to elastic photoprodnetion ofvcL'tor mcsons. In tlic s inni lat ion of proton dissociation llic valur of it was sct to thir 2.0for PYTHIA and 2 <f for EPSOFT Fignrc' 7.9 slmws thc nortnali/^l ,r, distribntions äsmeasiircd by tlic LPS foi data (open dots) and t l ic Monte Carlo in tx tn rcs ( f n l l doLs). The-f;, spcctruni brlnw 0.98 can bc explaincd by proton dissocialivc cvcnts w i i h a Icading prolon.
„ 12.5X
12.25
12
11.75
11.5
11.25
11
10.75
10.5
10.25
10
Figur«; 7.8: Tlic \ ditfcrciKT (NDF=11) nctwcpn data and Monte Carlo (PVTHIA) fortln: FCAL cncrgy distribntion äs a fmiction of n. The arrows indicalc tlic valncs for ncorresponding to a cliange in ,\ by l iinit.
()n tlic nppcr plot of fignrc 7.9 PVTHIA was nscd to simulatc proton dissociatiun nnd imdir Iowcr plot EPSOFT. PYTHIA dcscrilies llir clüta nuich bctter than EPSOFT. In table7 2 Ihc frnctionsof cvcnts witli a Icading proton in tlic LPS with T/, < (i.98 (LPS lag), a tagin thp PDT (elfter applying all clastic p" sclcction cuts) and n tag in FCAL, dcfincd abovc,arc summarizcd for data and llie Monte Carlo inixtiirrs. Tlic systcmatic errors 011 tlir MonteCarlo fractions wen- dctcrniiricd by changing tlir valuc of n bctvvrcti 2.0 and 2.8. Sincr tlicSimulation of thc PRT in llir ZEUS ilctcttor Monte Carlo program ignorrd ilctcttor noisc,tlir tagging dlicicncy in tlic Monte Carlo was too high- Tlirrrfore the PFIT cfticirncics intlip Monte Carlo wert- scali'd down to tlic e[fieii'ncy mrasurod in tlic 199-1 data. Details nntlie torrcction pmccdure tan be fonnd in [ll|. In table 7.2 good agrceinent bclwcrn data
LPS tagPRT tag
FCAL tag
data1.3 ±0-1%6.7 ± 0.2%1.2 ±0.1%
PYTHIA1.3 ±0 1 ±0.1%C.2±0 .2± 1.5%1 . 7 ± O . I ±0.6%
EPSOFT1.9 ±0.1 ± 0 2 %8.9±0.3±1.1%1 . 0 ± 0 . 1 ± f l . 4 %
Tablc i.2: Fraktion uf cvmts willi a Icading proton in thc LPS of ij, < 0.98 (LPS tag), alag in tlic PHT (afler all clastic p° sdcction tnts) and a tag in FCAL for data and thc t woMonlc Carlo riiixtnres.
X•D
10
-1-10
-2
100.5 0.55 0.6 0.65 0.7 0,75 0.8 0.85 0.9 0.95 1 1.05 1.1
PYTHIA XL
10
•o '"Z.
-10~
-210
-310
l J t
s'0.8 0.1 "'
EPSOFT
0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1 1.05 t.1
X
Fignre 7.9: Kormalbrd LPS T, s|)crtriiin fnr dala (open duls) ;ind Mmilr f'ailn mixtnrcs(80% elastir, 2<l% proton diüsocialiim) iiftur all das t k- ;>" si-lirtinii cnts (iiirliiding P* < ü.üGc\' )• On t hl1 upper plot PYTHIA was used to dcscrilie prolon di.ssonalion <ind on tliclowr plot EPSOFT. Otily tlic statistiral crrors nre sliown.
and PYTHIA is srrn for llit'cvent frartir.ns tngged in LPS and PRT, ivhnras HPSOFT d.jesnot dwcribc ttie data. On the olber liand EPSOFT agrecs wilb tlir dala in die fractionof eveiits taggcd by FCAL, whereas in PYTHIA this fraction is liigliei llian in tlic data.Prolon dissociativc cvpnts taggcd in tlic PflT and in FCAL leavc only a sinall anionnl ofcnrrgy in thcsc detect<irs. Thercforc a rorreet siinulation iif the forward n-gion nf Mie ZEUSdcttTtor, concerning for cxatnple inactivc matcrial, is vcry itnportanl for tlic clfidnicy oftlicsc tags. Mure stndics arc nccded to detcrminc, wlietlicr tlic (liffcrciicc.s liclwccii dala andMonte Carlo arc due to tlic Monlc Carlo model or dne tu an ineorrcrt <letcctor siinulation.
Proton disüucintixT Monte Carlo cvmts ean also be nscd tfi dctcrinine tlic arreplancc corrcc-tioii for tlic mrasnred Pf distribntion tagged liy PftT (or FC'AL) Tlic arecplance correctcdP72 dislributiun cnn bc correctcd tu |/| nsing a rom-ction fnticliun, calmhilcd funn ihr MonteCarlo samplcs for prolon dissociation. Fignre 7.10 sliows tlic eorreetcd tlN/il\t\nfor proton dissociativc cveiils, nsing tlic PRT tag and EPSOFT for tlir nirrrrlions. A lit
10
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
Itl (GeV)
Figurr 7.H): Tlic corrocted ]f| distribntion for proton diswirialivc cvctits. Tlic PRT lag wasuscd l» identify proton dissotiation and EPSOFT for llic acccplancc corrcution. A fit withan exponcntial yiHds a slopc of b = 5.8 ± O.C GrV~a. Only thc statrslical crror is sliown.
wilh the fnnction rfA'A/|f| = /»r'*1" yields:
b = 5.8 i 0-3 stal. ±0.1 syst. MC ± 0.5 sysl lag i fl.2 syst. n OV~7 (7.10)
The first systcmatic crror givcs thc dcpcndrnec on thc Monte Carlo uscd for llic acreptancccorrcction, the sccond systcmatic crror thc dependcnce on thc tagging niethod and the thirdsvsicrnalic crror thc dcpcndcncc on thc valur on it. This rrsult is again consistent with thccsiiniatc givcn in [ö7| nainely b-,p^p»\' ~ 0 äft,((r»/i). Mcasurnncnts of btl(pj>) at ,/s w 63GeV yicld b,,(pp) ^ 13Gc\'-J.
The mcasurcmrnl of thc contribution of proton dissociation to tlic ctastic p° signal (Cpdi, =21) 3%t*f%) allo«ed also a dctcrmination of ihc ratio of thc cross seclions of clastic andproton dissodativc p° photoproduction for PT2 < 0.5 Gc.V!. This ratio is givcn l»y:
<^_ = N*.l,t. = ( l - C .)/<... {7J1)
wlicn1 fr„ and f,.,,,. arr llic rfficicncU's of thc clastic p° sclcction cuts for clastic and prolondissofiativc cvcnts Thc cfTicicncy fB H„ is catculatcd ivith Monte Carlo gcncralors EPSOFTand P^'THIA in ivlni-li pro ton dissociativr cvcnts liavc a hadroniu niass MN in tln1 ränge(MP + 'IM.)'1 < Ml < I).l»'*p. \Vli i lclhcdalacxIcnds dnwn in MN tu JI/„+A/., tlic lack ofsirnidalrd cvcnts lictwccn MF + M, and ?Lfp + IM, is not rxprctrd t o liavc a significanl cfft'd|-18|. Sincc („6„ ilcpcnds strongly on n, tlic rcsull for tlic C.THSS scctmn ratii) <lcpctnls on n
4 5
3.5
2.5
2
t. 5
0.5
o 1 >- ..L3
n
Fignrc 7.11: Ratio of tlic rhistir to proton dissuciiitivt* /'° cioss scction äs a fmirlion of n tistidin thc Simulation of proton dissocialion l>y P^TI^A (fnll dnts) or EPSOFT (opcn dols).
äs well. In figurc 7.11 or,./(7pjl, is shmvn versus fi for EPSOFT (opcn dots) and PVTHIA(tloscd dots). Thr crror bars arc givcn by thc stalislical crrors of <,,., ff ,,„ and tln; crror onCf,,„. Thc rcsult is ahnost indcpciulcnl on thc Monte Carlo generator and nsing a vahic of7i - 2.24 yiclds:
— =2.0 ±0.7 (7.12)
H;ntf ; i r t r imf .s Ic l f i ' ^
Chapter 8
Low Energetic Pions in the ZEUSCalorimeter
In tliis chapter ihr cncrgy deposilion u f t h c pions from die p" dccav in the ZF.l'S calorinictcrwill bc comparc.d lo lest bcam results. \\dercas in tlic lest bcam nionient i ini selrclcd pionsarc dircctly scnt onto tlic calorimcter, in tlie ZEUS cxperimcnl tlic pions, af tcr bcing nioiiion-tun i analyzcd in tlic CTD, Imvc to traveise inactive mater ia l bcforc h i t l i ng the calorinicler.
8.1 Pions from p(} Decays and Test Beam Data
Sclcctrd clastic p9 evcnts in tlic ttuiss ränge brUvecn ().'>') OoV and 1.2 G<-\ WCIT nscil t«stndy tlic cncrgy drposition nf ]i»\ i i iuni i ' i i turn pktns in llic ci i luri tnctcr . Sitirc du1 FI,Tri'qiiircmcnl uf 4G'l McV in REMCpi.-i cniiws a liiiis in Mir nn-rgy d i s l r i b t i t i o n of tl ic piimsc\cnls in wliicli llic t wo pions l i i l uppositc C'FLT IripRrr rrgiotis \VITC nscil in diis shirly.After rcquiritig that onr piun Iriggcrcd tlic i'vcnt (die C'FLT IriRgcr rcginn liil by tliis prnnfircd) thr. otlicr pinn is nit tinbiast-d trst pion. As cxplaincd in strtinn 4 ,1.2 t l i c <-iicrgy ina conc around the track impact point on dir calurinic-lcr, with a radins <»f -10 cm in llicclrclruniagnelic scctron and 05 cm in tlic luulrnnic scttion, was assigncd tn t l ic pions. Tlicradii wcrc choson tu makc snrc diät an cncrgy dcposiliim ontsidr t l ic hvu nincs, was notcauscd by the pions. So all llic rnetgy dcpositi'd in tlic calorinictcr by the prnns is insidelliosc radii. Tbc conc si/c is also consistt-nt with die facl llial 0")% of tlic energv in a tu»dn>tishowcr is containcd in a radins of l A0 (\ = 1(1.8 cm for the ZEt'S calminictcr) .
Tlic cnrrgj' insiilc ihr conc KCM, was stmlicd äs a fnnrt i im tbe kincl ic ciicrgv E*,,, of die
pions. The kinetic cncrgy is givtin by E*,,, - Jp'2 + A/* — <U„, wherc ;i is tlic pion n io i t ten lnmnicasnrcd by the CTD. The kinct i r cner^v was uscil, sitic-e at Iow euergics die eneigy respon.seuf a calorinictcr for diffcrenl particlcs is csscntially a fiuiction tif EI,,,, [45|.
In tlic uppcr plot of h'gnre 8.1 die rat io E,-.\i./Et„, is plnlted vctsns Ek„, for posilivc aminegalivc pions frotn (in (kx'ays. Tlic ratio is oblaincd from t l ic meaii valne uf a fit w i th aGnnssian to tlit; £f^/./Et,„ distribution in bins of E*,,,. A clear diffcrcnrc is seen bctwecnpositive (fnll ilots) and negative (upen dols) pions. Tbc rat io iticrcases äs diecrn'rj;y tiirreasesn p to kinelic cncrgies of ~ 500 McV and t heu s lar ts t o dt-crcase. A valuc < > f — 0.8 is rcai'hcilf1"" F-k,n = 1-8 GcV. E,-.\i,/Ei„, was a ls t idc teni i ined from lest bi-arn da l» [-("i] for |K»sitivc andnegat ive pions and is sliown in die lowcr plol uf f jgn re 8 1. For lest beani d a t a E,-M.IE^„,
UJ
LJ
1.4
1.2
1
0,8
1.8
1.4
1.2
1
0.8
0
0
(GeV)
(GeV)
Figt irc 8.1: Ratio of thc cncrgv deposilimi in tlir caloriinetrr ECAI, ovcr thc. kiiielk riicrgyE i,,n äs a fimction of E*„, for piuns äs meiisnrrd in ihr ZEUS dclrctor (nppcr plol) and lestbcam data (lowc-r plot). Thr ratio is shown for pusilivc (ful l syinbols) and negative pions
symliols) scparatrly.
in räch hin of E*,,, was dctcnniiicrl frurn tho mcati vnluc of a fit wi th a Gaiissian of t l i r pulsehriglil spcctra, unclrr ihr asfiinnplion ofpiTfrt'1 l incari ty of thc Ciilurimctrr wi th a calilirationtonst it n t of (Q)/]> - 16-24pC/GrV. Tbc Irst bc-atn data was takcn without inaclivc niatrria!in front of thc cnloriincttT. Thcroforr t l ic ra t io EL-Ai./Etin is higher. Tlic ratio di-rn-ascsfor incicasii iR kinctic trncrgy and rcachcs a valuo of l for k inr t ic cucrgics aliovp ~ 2 Gi'V.Also in Ihc kmrr plot of (igurcs 8.1 a dilfcrcncc hctwrcn positive ( f u l l sqiiarcs) and negative(o|K-n sqnarcs) pions is sccn.
Tlir rffi'cl of thr chargc difTcrencr can clrarly br sccn in figurc 8 2 and lalilr 8.1, wli icl i shmvE"-AIJE[.^, for pions froin ^° drravs ( f u l l ditts) and tcsl bcain dala (opt'ii dols) The cffrctjs milch biggi-r for t l ic pions, moasurnl in tho ZEl'S cxporiinent w i th inacttvi1 m a l r r i n l infronl c»f tho cii iorinicttT. Thr riicasnrcd differonn1 is up to 1.1% i i t Iow nirrgy and decn'ascsfor iiKToasing k i n c t i c fiiorgy of ihr pions. For t l i r li-st licani daNi t l ie d i l fe rnne is s i iui l l iT(only i i j i In G%) iiiid viinishes fnr very sinall k i n c t i c encrgirs. For cvcnts • i in i id i i l ing o l a s t i c
I. l'ttini fnilll /_/' -.t ,-!»(> Irst Brviltl I)nt:l 89
UJ
Lü
1 "
1.15
1.1
1.05
1
0.95
ü.9£
-i
ii
-' T +
0 * |
fS o °
-
) 1 2E«. (GeV)
Figurc 8.2: Ral io of llic cnergy dcposition of positive ,-md negative pions in thc calorinietpräs a funclion of Ihc kinctic cncfgy for pions froin pn dirnys ( f u l l dots) and test bcam data(opcii dots).
p° pholoprodnclion, whith \vtrr passcd llirongh thc ZFJiS dctcctor si tnidation prograrnMOZART anr) solcctud likr the data cvonts, tio differencc in thc cncrgv dr-position botwronpositix'c and negative pions was fonnd. So thc chargo dilfen'ncc ;ilroa<ly sren in the lest l>eanidata is not sitmilatcd in MOZART.
£„,,.(GeV)0.26003550.450n.cwiU.840
1.20»1 820
TT»* / r«-L'VAI.IZ'CAI,
pn dccfiys
l.lliO.OG1.13±0.(131.10±0.()2I.(l9i0.02107±0.01l.fHiO.Ol1 OliO.OI
Ek,n(Ge\-J
0.380
O.C24
0.871
1 .3(57
1 .8(iG
r** /F""l'CAt.l '-CAI.
tosl bcam data
l.DliO.Ol
I.OG10.01UMiO.Ol1.0110.011.0210.01
T;ilile 8.1: Rat io of tho cnorgy deposition of j ios i l ivo a n t l iicßiilivc pions in the caloi i tuc terfor pions frotn fin docays (Icfl n i l i nnns ) and toM l iea tn data ( l i g l i t n i tmnns) .
.-< L<>» / • . 'n r i f j i ' f r r l ' i tu is i» tlf XKI 'S (Vi
Chapter 9
Results
Elaslic p° pholoprodnction can lir cliaracleri/cd in Irr ins »F a fc\ variables. In th is chaptcrthosc distr thutions nscd lo describe /)° pholoprodnction wil l In: sliown, nanir ly thc inassdistr ibntion, ihr \1\i and t tu- dtray angnlar distribi i t inns. Thc clastir pn plto-toprodurtion cross sce.tion wi l l be extrarted froin t In- mass d i s l r i l w t i m i In thc firsl twoscctions of tliis chapter Ihr atiTcctinn piiK-cdiur and thc systi-matii- chccks arr introdnccd.Most of t In; rcsults shown is thc following srctions, includi t ig ihr systcniatic crrors arc suni-niari/.cd in thc lablcs in Appendix C.
9.1 Correction Procedure
Thc diffcrcntial cruss scrtions, shown in thc fnllowing scctions. wert' cv;dii;iU-d in cach hin ofthc variable v äs
da A',.' (n 11
l '
\vherc Nv is thc nnnilicrofoljscrvcd cvcnf.s in Ihr bin 13 aflrr backgronnd snl i t rac l ion (thajitcr7) and torrfctioii of REMCn.i triggcr cllicicncy (scction G. 1.2), t is ihc ar.cc|)tancc in thcbin, C thc intcgratcd Inminosity, ^ is thc rhVctivc photon llnx <f(]i,Q2} (nination (3.54))intcgratcd ovcr thc Q7 and H'1p ränge covcrcd l>y thc sclcclion and Aß is ihr bin-width. Forllic corirctiiMi inethod (a) f takcs jn to iuronnl thcgcimict r ica l acccptancc and t h c sincaring inthc variable v <inc to tlic dctcctor rcsolntion. In an altrrnalivc approadi (corrcclion nu-thod(l i j ) ihr acccptancc is givcn hy ( g , thc pure gcomctrical iit-ccptancc, and i h c sincaring istakcn inlo accinmt in thc fit fnnct ion applicd to Ihr corrcctcd data (sct-tioii (i 2). Corrrtrlionnicthod (b) WAR only applicd to ihc im'a i iant niass disti ibntion für thc wholc saniplr andin H'lp bins. Thc statistical crror of ihc <lilfcrcnlial cross scctinn da/du is gi\en by crrorpropagalion of thc slalistical t-rror of (VB and ihc stalistka! crror of ( (or f 5 ) . Dilfcrcntialdistribulions will bc sludicd in H"1P, A/,*»- and l f | bins. Sincc in thc analysis prcscntcd inthis thcsis, thc ontgoing clcclron and proton wcrr not mciLSiircd, |/| cwild not lir dclcnnincddircctlv. To stndy thc |f| dcpcndcnc*1 of Ihc niass and dccay angular distribnlirms, thccvrnts wrrc sclwtcd in Pf- bins and thc ncrcptancc i was calrnlatcd taking in t i t acconnt t.hcdilfcrcncc bctwccn P7J and \t\. In this way ihc torrrctcd dilfcrcnlial d i s t r i ln i t ion in a ccrtain!/| bin was dclcnnincd n.sing a rorrcctinn, lo ai.-foini( for l.lic fatl that Q7 is nini-/cro, whichwas cvaluali 'd f n i n i thc Monte Carlo si innlal ion. In Ihc following scrlimis leasl sqnare fits
C'fi;i/Jfa 'J.
to tlic Mit1 corrcclrd dilfrrciitial distribtitions will be pcrformcd. In llicsc Hls the quantily
2
,3 (9.2)
was niininiJ7cd. /(K,n) is Mie fundional bcliavior expected for da/dv. This fiinction tippend
on Mic paranii'tcrs n. These paramctcrs describc ccrtain proper t ie.s of claslic p° photopro-dnction. A/Jjh,., is tlic bin-width uf bin i, do/dr\,„„i tlir diffcrcntial cross section in bin iand (Wa/dt?|hlfli it's statistical crror. The simi runs over all bins insidr the (Strange.
9.2 Systematic Error
Thr systcmatic error diic to a certain cffcct was delermincd Tor niost contribntiüiis by chang-ing cuts applied in the analysis or changing thc rcwcighliiig factor applicd to Mic data. The37 systcmatic checks pcrformcd wert* groupcd into 12 classes. Thc following list describcstlic 12 classcs (i to xii) and the 37 systcmatic checks (l to 37) considcred in this analysis:
i. Tlic tracking systcmatics was detcnnined by chariging thc qiiality cnts imposcd on thctwo tracks (section 5.3).
1. No trark qiiality cuts werc inipospd.
2. Tightcr track qtialily cnts wert' applied (|r/| < 1.8 and P, > 200 McV).
ü. Thc systcmatic error due to thc proton dissocialivc background subtraction was dc-tcnnined by changing thc rewcighling factor (cquation (7.ü)) applied to thc data. Thcrcwcigliting factor depends on two paramrter, Mic slopc b„,„ and the absolute normal-i?,ation N, wliich wcre dclcnnincd indepcndently.
3. Decreasing thc normali/ation N insidü thc error (cquation (7.G)), thcreby dccreas-ing the anionnt of proton dtssociativc batkground.
4. Increasing thc paramctcr N.
ü. Increasing thc slope dirfprcncc b*,„ inside tlic error (cquation (7.3)), whilc kcepingthe absolute anunint of proton dissociation background unchangcd.
ß. Decreasing thc slopc differencc bd,B inside llic error, whilc kceping thc absoluteantount of proton dissociation background unchanged.
iii. Systematic error due to tlic RCAL effiriency reweighting (stiction fi.I.l). Tlie RCALtriggcr cfficicncy was determincd froni data by nieasuring the prohability for a pion toUiRgrr an cvcnl. This probability was dctcrmined froin data wild a certain stalistiralan-nracy. Thc error of ihn rnwcigliting factor is givcti by error propngation froin thestatistkal error of the probability for a pion lo triggcr an cvent
7. DcrrriLsing thc RCAL triggrr cfficicncy, inside the statistical error, tliercby in-c-rcasing the rcwcigliting factor.
D.2. Systciiiafir littor
8. Inrrcasing tlic RCAL triggrr clficicncy, thcrcliv dcrrcasing thc rc-weighting fartor.
fiv. Model flepcndcncc of tlic iicceptance dcterinination by chnnging thc distributions in
M\P, |(|, M„*w- and thc decay anglcs in the Monte Carlo Simulation within theirunccrtainty (ö.2).
9. Increasing tlic paramcter rjj, Wr°J and r°l,. d<-srribing the decay anglllar tlistri-bution.
10. Dccrcasing the paramelcr r^, SrftJ and r]".,.
11. Increasing Mic paramcter n, uscd to paranicleii/.t: tlic II'1P distribntion.
12. Decreasing thc paramelcr «.
13. Increasing thc paramcter b and r, uscd to paramcterizc thc |/| distribntion.
14. Decreasing the paramcter b and r.
15. Increasing the paramcter it| and n2, uscd to paramclcri/c the shapc of the invari-ant mass distribution A/,»,-.
16. Drcrcasing the parameter ri| and tij.
17. ricweighting thc decay angular distribntion according to s-channcl hclicity con-sevvation, iiamely f?r°Q = 0 and r°t, = 0
v. Systcmatic error due to a change of Mic valuc of (2, nscd to parfimclci i/c thc ratio uf
thc transverse to longitudinal cross scction ot.ja / - f,2Q7/M7n The purametcr £2 isnceded in ordcr to rcwcight thc Monte Carlo Q7 distribuMon and in thc calculation ofthc Hux factor (equation (3.Ü3)).
18. Assuine (,J = 0, (lins ncglccting tlic longitudinal I.TOSS scclion (r,_.
19. Assume^2 = 1.
vi. Systcmatic error due to a cliangc of Mir maximal f^2 of Mie data Q7„,ai. Q*nai wasdctcrmined froni a Munte Carlo Simulation to bc Q7nai = •! Gc\'2. Pur this systcmaticcheck thc valuc of Q*nia was changed in l IIP. Monte Carlo Simulation äs well äs for tlicdetermination of £2 («juation (5 G}) and the flnx factor (cquntion (3.53)).
20. AssumcO?„„ =3 GcV2.
21. Assumc Q2mai = 2 GcV2.
vii. For thc mass fits in IlTlp and |f| bins tlic p° mass M^ and thc widtli P0 wcrc fixcfl
to thc values äs dclcrniined from h'ts to tlic wholc spectrum. In l>ins of 1V>P also theamount of skewing givcn by \D/A\n cquation (9.7) and n in crniation (9.10) was fixcd.For thc fits to thc |f| distribution in H'1(, and jU„t„- bin.s thc parainetcr r (equation
(9.14)) was li.xed to thc valuc äs dctcrmined froin a fit Mie thc wliulr |/| distribiilion.
22. Increasing the fixcd valuc for A/^u and PD inside thc statistical crror givcn liy thclit to thc whole distribntion.
23. Decreasing thc fixcd valuc. for M^ and PQ
9t C.7iapf.cr!). Jtcsiills
24. Ini-reaMiig Mir Hxcd valnc Tor |/?/.-l| n in l n inside ihr staltstical error givcn by tliclil (o Mir wholc distribiition.
20. Decreasing thc (ixcd \a luc for \B/.-\\d 'i.
2G- Incrcasing t l i r fixer! value for r insidr t IIP slatislical crror givcn liy OK- fit to ihcwliolc distr ibntion.
27. Decrcasing ttu1 fixcd valne for r.
These systcmatic chccks have- no clfecl for tlic rcsulls dcrived from thc dccay angulardistribntiotis.
v i i i S\stcmalic crror dnr lo a changc of tlic fil proccdnre to tht1 \t\n in Mtt,-and H'7P bins
28. Thc paranictcr r was not fixcd, but tlic absolute normalization of tlir |(| distrihu-lion (.4 in eqnalion (9 .M)) was calculaled äs thc integral ovrr thc invariant inassdistribiitioii.
29. Considi'ring the c ;ind A ;is a frcc paramoter.
These systematic chccks havc nocffcct foi thc mass and thrdecay angnlardistribiitioris.
ix. 3l). Systeinatic chango dnc to a dcrroases of thc fit ränge. For /U.»,- the ränge n.G< A/„ + „- < 1.1 GcV (nominal-. O.ü5 < M*>,- < 1.2 GcV) was used, for cos 0,, the,ränge -0.8-1 < tost?,, < 0.8-1 (noniinal; -1.0 < cosfl,, < l.tl) and for cos t?,, in the(wo dimcnsional dccay angu la r d i s l r ibu t ion Ihc ränge -13/10 < cos l?,, < 13/15(nominal: -1.0 < cos0,, < 1.0).
x. (.'hange in tlu- I t inn ing of the niiiss d i s l r i l i t i t i o i i , tht; | f | distribntion and thc detayangular disthliutions (nominal binning: tahle -13).
31. Morc hins (bin-width IG.6 MrV in A/,. .- , 2/35 in cos0h and T r / l T j in #/,).
32. Lrss bins (bin-width: 50 McV in A/ ,* , - , 2/15 in tos(9h, n/5 in 4>h and > 0008GcV2 in |/i).
xi. Systnnatic errnr dnr to a change of thc Breil-Wigncr f i inct icm and the nionientumdepciident widt l i uscd in the fits to thc inass distribntions.
33. Brcil-NVigncr givrn by (9.3) and widlh given by (9.G).
34. Brcit-\\'igner given by (9.5) and width givcn by (9.4).
35. Drcit-Wigncr given by (9.5) and widlh givrn by (9 G)
Thrse syslematic changcs have no cffett for the dccay angular disLribntinns.
x i i . For corrcction method (b) thc resolntiun, assiinied in thc ronvolitlion of thc resotutionfimction and the funcliun describing tlir physics, was changed.
3ß. Increasing ihr rcsulntion äs givcn by Ute paramoler P] and P5 in criuation (4.7)l.v 25%.
i). .t i>f thc fitvaji'.-»it Ati-uts Distribution
37. Dccreasing the rcsolntion by 25%.
FnrthiTSoniceHof thc syst emal iccrror, wnidi havc an inl l i ici i rfon l hc absolute nurmalizationof thc tross scttion onlv, havc bccn takcn in to iircount in sirtion 9.4
• tl ic systctriiitic uncrrtainty in Ihr Intninosily nicasiirniient of 15%. [84],
• thc elfcct of elcctron initial am! final statt1 radiation and of vacnnm polari/ation loops.Tlu1 si7t> of tlie correclinn was estimated to bc smallcr ( l i a t i 2% [00] The cffcct ofradialivp corrections on tlic shape of the A/,..-,|(| and a t i g t i l a r d i s t r i lmt ions arc ex-pcctci) to be ncgligible. Ko currrction was applicd to thc cross scction, instend a 2%contribuliun was added lo the syslematic error
Fnr all thc rcsults qnotcil in thc following, the systematic crror was dctcrinincil in thc follow-ing way. For cach class (i to xü) thc biggt-st positive and negative dcviation froni thc i iontinalvaluc, dnc lo a singlc check in t Ins class, was nVlerrnimtl. Tlie t o t a l positive and negativesystematic crror was culculalcd äs a qnndralic snm of thcsc- dc\s u\cr all dasscs. Sonicclasscs do not alfct't all resnlts, so lliey werr not inchidcd in thnse resnlts ivhirh ihcy cannot alfcct.
Somo paranictcrs will bc detcrniined in cight A/ B 4„- and ninc \l\. For a fcw systematiccliecks big fluctuations from bin to bin in A f „ t „ - and |f| wen- obscrvcd. The reason fortliese fliictiiations nie stalistical Hnctuations in the dala and in the MnnU- C'arld for the.sesyslematic chccks. To overcome this problem thc systematic chedts wen' performc<l in onlythrcc bins in A/ w t , - and |f|, which are combinations of Ihree (in onc i-asc (wo) original bins.Thc positive and negative systcmatit: crror f<>r cach class was drtermined in tln-se llirce binsäs bcfore. These crrors wcre extrapolatcd to the finer binning by pcr fonning a (it of a l inearfimction in A f „ . „ - (or | f | ) to thc criors detcrniined in Ihc three bins. Tln- f i n a l positive andnegalix'p systpmatic crror in (he f iner b inn ing is again givcn bv l he (|nadrat.ic snm of crrorsovrr all classos.
9.3 Study of the Invariant Mass Distribution
Fignre 9.1 shows tlie differential tniss scction dn/dM.i,-, rorrertrd by method (b) in tlickincmatic ränge |(] < 0.5 GcV7 and 50 < ll"1p < 100 GcV. Thc inass d is t r ib i i t io i i is skewcdcompared to a Brcil-U'igner distribnlion, namely theie is an ciihaiiccini'iii of ihc low inasssidc and a supprcssicm of the high inass sidc. This skewing of Ihc TT-^TI" niass shape wasalrearly olwcrved at Iowcr cncrgies |H)|. At low cnergies a distortion o l" t l ic mass shapc atihc u> mass, dlic to p - u inlcrfercnrc, was obscrvcd. This cffect wil l be discnssed at cnd ofthis scction.
Variotis prescriptions wcrc pnblishcd in ihe OO's and 70's lo cxtract ihc "p"" out of theinvariant 5t*"n~ mass spectrnm. Unfortnnatcly thc resnlting V" cross si'ction depcnds onIhc prcscription uscd in thc analysis. Thcrpfore in this analvsJs d i f l e ren l presrriplions werefith'd to the mass disiribulion and Ihc resnlts wcrc compared. Mass fils were pciformcd toIhr spcctruiti shown in figtire 9.1 äs well äs in H71P and |f| bins
-10-L1_|J-1 1_l..-.' / . . . l . . . . l . . . . 1^^ . -L. .J-
1 1.1 1.2* (GeV)
Fignrc 9.1 Tlic diffcrcntial cross section rfo/rfAf.*.- in tlic kincmatic ränge |/| < 0.5 GcV1
and 5(1 < U\ < l Du GcV. Thc points rcprcsent tlie data and thc curvcs indicatc thc rrsult oftlic fit using cxprcssion (9.7) in thc mass rcgion 0 55 < A/,»,- < l .2 GcV. Thc dashed curvcrcprescnts thc rcsonant contribntion, llic dol-dashcd curvc Ihc non-rcsonant contrihntionand the duttcd curvc tlic inlcrfcrcnrc cnnlribiit ion Onty thc statistical crrur is sliown.
All thc niass fils prcscntrd in this section wcrc pcrfornicd in thc mass ränge 055 < A/„ .„ - <1.2 GcV. Tlic rcsonance in tlic n+it~ spcclrum was paraiuctch/cd by a rclativistic Brcit-\\'igner funclion
nhcrc M^ is thc noniina) f)° mass and P^o ihc niomcntuin dcpcndcnt width [58)
\- r* B - } = I 0 l —1o
(9.4)
whcrc FD is llic w id th of tlic pn, <l' is thc -n n imncntni i t in thc 7r + Ti rcst franic and qf, is thcvaluc of t]' at (lic p° nomiiml niass A/,». For llic systcnialic crror analysis (syslcinatic chccks33-3")) tlif follcnving a l t e rna t ive rxprcssions for thc Brcit-Wigncr fimction
(9.5)
!)..'(. Stutly of tlir Invariant A/am üistrlhutivii 97
P
(a)
(b)Fignrc 9.2: Dtagranis ci)rrrs[HHi(ting to thc tlin-c pmccsscs cunsidcr in tlic Swtiitg rnodcl,nanicly (a) rcsunant p° production and (h) nun-rcsonant n*v~ pruducl inn.
itnd thc width
(9-6)
ivcrc nscd. Tlic exprcssion (9.5) was nsrd in prpvinns ff photoprodiictitm cxpcriincnts,c.g (94). Tlic kincnuitic fiictor \/q' inlrodnccs a skcwiiig in t l ic Drcit-Wigticr fnnct ioTi . Thcii iuHicnt t im dopcndonl width in cqnation (9.4) ivas fonnd in lowcst ord(.-r pcrtnrlialiun thctiry,wlicn-as cquation (9.G) is an cmpirical form of tlu- width |ö8|.
A niüdcl oftcn us«d tu dcscril»1 Ihc tnass skcwing was first pointcd out l»y Siiding (MHj .In this inodcl ihr n*«~ pliotoprodnttion amplitudc is writlcn äs a snm of a dircctly pro-duccd Brcit-Wigncr shapcd p° plus a non-rcsonant batkgrnund |38]. Figurc 9.2 show thcdiagrains considcrc.d in this approach, nanicly thc rcsonani p° prodmition (a) and tlir twonon-iTSOTiant conti-ibiitrons (1>). Thc asyninictry of Ihr invar iant massdis l r i lmtimi is givcn bytlic intcrfcrcncc of thcsc two tcrms. C;dciilations hascd on Ihc Soding inodcl wcrc pcrformcdby Söding [101], Krnss JG5], Pnmplin |8G|. Rcccntly Ryskin and Shabclski |88] talculatcdtlic rcsonant and nun-rcsonaiil amplitudcs in thc casc of />" photo- and clcclroiirodiiction.
The Sikling model was vcry smrcssful in dcsciibing varions aspects of p° photoproduclionc.g.[9l, 93], l ike (he dccrcase of skcwing for incrcasing j r | and thc depcndenre of the \t\con M w t „ ~ . fü r t he pmposc <>f this anahsis the following simplificd prcscription of the massshapc, according to thc Söding model was nscd:
rf(T
<i.M,,
n• ~~r (9.7;
Thc nmi-resonant ampliliidc is denolcd by D and is assnmed (o bc Konstant and real. Thischoice is motivatcd by thc calciilation of Ryskin and Shabclski [88], who found that thcnon-resonarit conlr ibution is n Iniost f la t in A/,».- for the kinematic ränge of thc 1993 ZEUSp° photoprodnction analysis, Comparcd to (he 1993 analysis the kincmalic ränge in thisanalysis was incrcased in H',,,.
Thc tcrm f,-s - / l rx( l -0- t - 1.5A/. + , - ) in cquation (9.7), which is also prcscnt in all othcrmass paranietcrizations nscd in (his analysis, accounls for residual background from -j anddouble dissociativr pholoprodiiction (scction 7.3).
Altcrnatively the following paranictcrizalion, according tu thc Söding niodcl, proposcd bySpital and Yen nie [1(I2[ was uscd:
(9.8)
Spital and Ycnnic found that corrcction tcrms n\V(M,t,- )C, (A/^,,, - A/^,)/Af^, with
i > 3 have lo bc added to c(|iiation (9.R), whcrc nei ther thc siw and nor thc sign of thccini t r ibut ions C, can bc calcnlatcd. In a mass ränge rcasonably close to tlic p° mass onlya f i n i l c niimber of tcrms should bc ini |>nr tant Thercfore e(|iiatton (9.8) can bc rcgardcdäs an appniximat ion valid in a mass ränge closc to thc /i° niass. Thc tcrms C\gfor thc intcifcrencc and Cj acconnting for die noii-rcsonaiit contribii t i im arc treated äsindcpenden! parametcrs in et|ii;Uion (9.8). In fact lliis assnmption is not rorrcct and thercforef i l s according to ecnialion (98) can lead to iinphysical Solutions, naniely an interferencecontribii l iori which is bigger t h a n the sum of thc rcsonant and non-resonant contribiition atsmall niasses. This rcmark is also valid for othcr prescriptions of the Söding niodcl, uscd inf i l s of die invar ian t mass distribution, by variotis authors.
An al ternat ive approach to account for thc skewing of the n*it~ mass shapc was proposi'd byIloss and Stodolsky (87| Thcy ignore thc nnn-resonant backgronnd and instcad introdiicc amass Variat ion in thc produclion amplitndc of thc ff*. Dy relating thc proccsscs fp -t p°pand fßji -> fi°p togetlicr wi th a sinootliness assutnption thoy get:
dn(9.9)
For /in elccttoprodiiction, ROSS and Stodolsky predictcd that the niass skcwing fartor A/w ,*w_changps to (Q7 + Af ' ( i i . )~2 Thus the mass skcwing should Icnd tu disappcar al high Q*. Intlic ROSS Stodolsky model all n*^~ pairs are treated äs coming from p° iiliotoproduction. Atlowcr riiergies it was found tha t thc data could be described by a modificalion of eqnation(9.9). Thc following paranvlerization wil l be tlierefore used in this analysis:
da
dM.(9.10)
!!..'(. Sl\nly tifthr /mviii 'aiif Akiss 9U
wlieir /,/, is Ih r absolute noniiali/alinn of lliis picscriplion and n is treatcd äs a frcc pa-raincler. Tlic parainetcr n it i cqnation (9.10) caii he regarded äs ii mcasiire of tlic mnonntof skcwing. Tlic dccrcase of n with ' incrcasing \t\, äs nieasiircd at low cncrgies, tlms mcansthn t die mass skcwing dcrrcascs äs the iiioniriitnni transfcr incrcascs. In electruproductioncxperimcnts [27, 9, 61), 29, 18, 21, 39] i( was fouml diät n also dccrciiscs äs a fmiction of Q7.This bchavior is already cxpcctcd in thc IU»ss Stodolsky minie].
In tl ic f inal statc inlcraction modrl thc p" lucson is fonncd by a slrong linal-state intoractionof (hcp-wavc7r*7T~ pairs prodnccdby a process asshown in f i ß incÜ.2 ( 1 > ) . Kranirr and Qninn|G3| calc-iilalcd thc p° photoprodnction aniplititdc in this niodcl. Thcir result is essnitiaily:
(9.11),11
whcrc da*"/rlt is thc d i f rcr rn t ia l pion-proton cross .scction. For t = I) thc cnhanccment factorrcduccs to thc ROKS Stodolsky fiictor (A^/AfJ*..)'. Tlic fai-lnr (A/jL - 0*/(A/?*„- - O2 incquaf inn (9.11) rcsutls in a decrcase of skcwing äs ['[ incrcascs und a change of thc |(| slopc äsa tunction of M,tw-. The fiiuil säte interaction niodcl was extrndi-d to /»° ctrctroproiluctionby thc samc anthors |64], For the nnpolarized cross section thc niass skewing factor rhangcsto (jUj„ - t + Q*)*/(M*i„. - t + Q3)7. Tims in this model thc anioimt of skcwing rtccreascsäs |(| or Q* incrcascs.
Reccntl.v Nicsclcr, Pillcr and \Vii-sc (77] showcd tha t tlic A /„ t . - r l i s t r ibut iu t i for clastic p°photoproduction is dclcrniincd to a largc cxtcnt by thc two-pion ront i ibut ion tu thc pliotonspcclral function, äs givcn by (he pion form factor. Tlic bi t ter is knnwn t i> lu'gli precisionfrom r+r~ —» ir^n' i i n n i h i l a t i o n . In this process resonanl and noii-rcsonatit v*ir' stalcs areautomatically acconntcd for Thcy cxtcndcd thcir considcration to (P elcctroprodiiction atmoderate Q7. Using thc vcdor nicson doniinancc pi r tnrc thoy fonnd tha t thc niass distri-bution of TT*JT" pairs approathcs a svitinictric shapc with rising Q7. Tlic EG65 rollaboration[39] found that t l ic M,*-,- dis tr i lmtions in the Q* ränge ().!."> < (f < 20 GeV2 aro wellreprodua-d by this niodcl.
Thc analysis of thc di l fercnl ia l cross scction d a / d K f , t , was pnforiTied i ising corrcctionmclliod (a) (resoluliini taken int o account in thc aceeplance i) and corrcclion mcthod (b)(resolution taken inlo account by a convolutinn of thc fit fnnct inn w i t h a Ganssian). Thcdiffrrcntialcross scction do/<iM,i,- wasfittcd according t ( ic i | i i a t ion (97 ) (Standard SÖdmq),cquation (9.8) (Spital Ycnnir Söding) and cf|iialion (9.111} (ffo.'i.'; Stmtnlsky). In ligiirc 9.1thc resnlt for thc Standard Sodinrj fit is shown. Tablc 9.1 sninniiirr/cs llic rcsnlts derivcdfrom all thc h'ts to thc spcctrum for the (wo corrcclion mcihods. Tbc \'fNDF for alltlic f i i s is satisfactory As can be sccn froni thc table thc valne nf A/,/, and F0 dcpcndson thc prescription nscd to paramcteri/o the niass dis t r ibut ion Corrcction meüiods (a)and (b) gtvc similar rcsults for all thc Parameters, cxccpt for thc wiildi PO, which is biggerfor corrcction mcthod (b). The valuc-s obtaincd for the f>° niass are compatible wi th thcPDG vahic (AV = 768.1 i 1.3 M«V) (82], whcrcas the widllis diffcr from thc PDCi valut-(T0 - 150.9 ± 3.0 MeV). The statistical crrors of Ihr paranictcr arc s imilar , bnt Icnd to bcbigger for corrcction nielhod (b) in which bin liy bin rorrelations are properly lakcn intoacconnt. Thc amonnt of backgnuind undcr thc p" peak, äs givi-n by the parameter A,.5,was fönnd to bc sniall ftir all mass prcscriptions. Thc f i t t c r l valne of ,1;.c, corrcsponds to aniiUcgratcd contribution lypically smallcr than 1% of thc total for all the niiiss lils pcrfonnedin this analvsis
Siiditig
Af„u (MrV) l'o (McV) A2 (/.b) D/A (GcV-1«) -4/-S (GcV-1) X^INDFrorrrrtion nicthod (a)
770 ± 2 140 ± 3 7.54 ±0.11 -0.670 ± 0.1122 | 0.004 ± 0.1X12 0.73
corrcrtion nicthod (b)771 ± 2 159 ± 3 7.5D ±0,12 -0.70G ± 0.025 0.000 ± 0.002 07C
Spital Kennte Sötiing
A V (McV} l'o (McV) A0 (|ib) C, (GcV- ' ) Ci ( G c V ^ 1 ) | Ars (GcV-') X7/NDFCorrcction incth<id (a)
771 ± 2 142 ± 3 7.85 ±0 .10 j -2.58 ±0.07 1.87 ± 0.23 0.00 ± 0.01 0.52corrfction mctliod (b)
772 ± 2 155 ± 7 7.99 ± 0 . 1 5 -2.57 ± 0.08 1.83 ± 0.7G 0.00 ± 0.04 0.77
ROSS Stvdulsky
M,fl (McV) U (McV) /„" ((<l>) n A,.$ (GcV- 1 ) Xl/NDFcorrortion nicthod (a)
771 ± 2 138 ± 3 7.74 ± 0 . 1 1 5.13 ± 0 13 0 004 ± 0.002 0.42corrcclion tncthoH (b)
772 ± 2 150 ± 3 7. 87 ± 0 . 1 1 5.09 ± 0 . 1 4 0.003 ± 0.003 0.76
Tablc 9.1: Flcsnlts of the fits for llic two correction mcthods and tlic thrcc paranictcri/alionnsed in tlii.s analysis (stnndard .'i'örfiriffrtinalion (9.7), Spital Keimte Sörfiriflcqualion (9.8) andRnss SfodoMj/cqnalion (9.10)) Thc fils wcrc performed in l l ic mass rcgion 0.55 < flA,*.- <l 2 GcV. Thc crrors arc thc statistical crrors only.
U"TP binshmiT limit
50 GcVGO GcV70 GcV80 GcV
uppcr limitGO GcV
70 GcV
8(1 GcV10(1 GeV
avcragc54.8 GeV64.9 GeV
74.9 GcV89. G GeV
|/| binsto wc r limit0.00 GcV
0.01 15 GeV2
0.02G GcV2
0.045 GcV0.07(1 GcV1
0.1(H)Gc.V0.135 GcV2
0.190 GcV2
0.28 GeV1
uppcr limitD.OllSGcV0.026 GcV2
0.045 GcV2
0.070 GcV2
0.100 GcV2
0.135 GcV2
0.1 9(1 GcV2
0.28(1 GcV0.50 GcV
avcragc0.006 GcV2
0.018 GeV0.1)34 GeV0.05G GeV0.084 GcV2
0.1 15 GcV2
0.1 58 GcV2
0.224 GcV2
03i:>GeV
Tablc i) 2; M'lp and \t\s nscd in thc stndy of Üic invarianl mass dis tr ibnt ion.
'J.'.l. Stinly «f t In- lintuimtl 101
1> 0.84>
^•0.75
m 0.7
0.65
0.6
0.5%
~ . f
.
l * *L f
-
Ö~1^L"J~i60 ~~1~'~~ 70~L~~'~~J ^80 J~J~ l~1 go J~~l~'~~LJc
W„ (GeV)
Fignrc 0.3: Thc r f i t i o |fl/.4| for l l ic four U',, intervals. S! a l i s l ind crrors uii ly arc shown. Tliclinc indkatcs ihr valw dclcrniiiu-d froni ihc \vliolc sample.
The fits of tlic m:iss dis tr ibnt ion \vrrc rrpcalrd in fimr II'„, »ml n ine \l\. Tlic bin si/.rsarc givni in tablc 0.2. For thcsc fits tlic ;>" niass and widt l i wr-ro fixccl (o tlic vnlucs givtinin tablc 9.1. The valiu- of \B/A\ Söihng), which is ;i lui'.nsitrc uf thc nniotint ofskcwing, isstiown ;is n f iu i f l i im of I!'1(, (coircctinti miMliod (b)) in [igurc 9.;J. Only st;itistir;ilrrnirs arc sliown. No «Icpcndnire of tlicsr luiraiTictiTS on U"7r, c;m lic scrn \v i t l i in t l i is data.Tlicrcforp in thc folltwiiig also lltc anioiint of skriving äs givcn hy D/A in rqnation (9.7),C, and Cy in rqnation (9.8) nr n in rqiiatinn (9 Kl), wi l l br fixcd, for thc (its in H'1p bins.Figiin1 9-4 sliows ihr fl i l fm-uli j i l CTOSS scrtion <lo/(iM„*, for Ihc fonr \\\ bitis, corrcctcdby rorrcction mel l i fKl (b ) , ((iget her w i t l i ihc rcsull of a fit iiciording t o cqnaliun (9.7). Againthc daln is niccly tTpruduc-rd by thi; parainctf r i /aHdi i . Thc rcsnlts i>f llu- mnss fits in H'7P
bins wil l bc discnsscd fn r thc r in scclion 9.4
Tlic mnss d i s l r ibn t ion (rorrcctinn nicthod (a) ) in ihc n inc |([ bins is shown in fignrc 9.5tügclhcr wilh thc rcsnll of fits nccording lt> cqitntion (97). In tlii-.sc fils ihr inass and llicwidth of Ihc /i° wen- fixcd to thc valncs givcn in tablr 9.1. Thc niass dis t r ibi i t ions bcconicniorc Symmetrie äs |f| incn-ases, ;IF already obscrvcd nt tinv ein-igics [92, Kl, 1(14, 94, 95, 47,11)3, 4, 60, 80]- The rcxnlls fw \f3/A\d » frmn thc mass (its arc sliown äs a fnnctinn of \t\n fignrcs 9.6 and 9.7. Slatislical rrrors are shown by tlic inner crror bars and tlic outor crror
bars rcprcscnt ihc slnlistiral and systcmatic rrrors addcd in c|uadratiirc. Thc dominantsystcmatic crror is givcn by tlic crror classcs i and xi, iiaincly llio tracking systomalicsand a ehangc of ihc nioiiicntuni depciidcnt width uscd in llie inass fits. In lliis sludy llicsystcmatic chrcks 34 and 35 luwc lo bc cxrlndcd froin thc systcinatic crror calculatiun,bccansc part of tlic skcwing wi l l bc simply transfcrrcd In thc Drcit-\\'tgncr fnnclion forthcsc rhccks. Bntli qiutntitics \H/A\d n flccrcasc ivi th |/|, sincc thc skcwing ilwroascs ;LSthc momcntiim transfcr incrcascs. In h'gnrc 97 the rcsnlts arc cumpan-d with Iow cncrgynicasurrnicnts [9."i, 47| atid modcl predictidiis. Thr modd prcdiclions wcrc dctcrminctl äsfollows. Events wrre gcncratcd wilh a Monte Carlo program bnscd on Ihc modcl and wcre.bined äs a fnnctiuti of |/|. Tlic h'l.s pcrfornied to llic Mwt, speclra froin llic data for dilfcrrnt\1\s wcrc rcpcalcd for thc gencralcd events - In i t w i t h niuch smaller bins. The rcsnlis werc
1(12
Ü
-O60
40
30
20
10
00.4 0.8 1 1.2
M.„. (GeV)0.6 0.8 1 1.2
M.*.. (GeV)
70 80<W-<100GcV
0.4 0.8 1 1.2M„M- (GeV)
Fignrc 9.-1: Thc diffcrrntial cross scction dn/d/i!rt„- in diffcrcnt U'7p bins. Thc poinlsrcprcscnt thc ilaln and tlic rnrvcs indicatc llic rcsult of thc fit nccording to vqnation (97).Tlic (P rnass, tdc widtli atid thc aniount of skcwing äs givcn by B/A was fixcd lo thc valiirsprcscnU'fl in lablc 9.1. Otily llic statistitat crrors arc sliown.
parainctcri/cd by fiinclions, which arc sliown in figurc 9.7. Thp Söding modcl prrdiction wasdcicrminrd witliin thc framrwork of thc cakulalion of Ryskin and Sliabclski (85). Thc onlyfrcc paramctcr of this calcnlation, llic pion proton cross scction owp, was dctcrminpd fronia fil of thi- tnass distribulions in fignrc 9.ö according to llial niodcl |11G] Thc prcdictio»fur llic final Mate intcraclion niodcl was obtaincd by rcwcighting a Monte Carlo samplearcording (o cquation (9.11), including thr cffcct of non-^cro Q* äs discusscd abovc.
Tln' defic;i.se of ihr aniount of skcwing witli |f| äs nicasnrcd in this aiialysis is in goodagrecnictit with th<' mcasurcnicnts of fixcd largct photoproduction cxpcriinents, indicatingthal l he skcwing nf tlic ff inassshapc docs not dcpcnd 011 H'1p. As notcd abovc tn tlic prcscnlanalysis P72 is nieasurcd, which may difTcr froni |/| whcn Q7 is non-/cro. Thc Monlc Cailosiiiinlatinn nscd l(i rurrcct thp data docs not inclndc thc dccrcasc of skcwing äs a function of(f, obscrvcd in prcvjoiis clcctroptoduction cxpcriincnts Howcvcr for thp. P' bins considercdtlic nicdian and nvciagc Qy rliangc onty sligluly Tlic mcdian Q7 cliangcs froni ~ l()~s in
'.>..!. .Sfm/j- of tlir hiviiiiittit M.VK Distrihiiiioii
10
J
-2.5
> 10
0.0<lt l<O.OI15GeV1
0.75 1M.„.(GeV)
0.75 1M.«. (GeV)
0.75 1M«. (GeV)
10 0.07<ltK0.10GeV1 0.10<ltl<0.135GeV'
0.75 1M.„. (GeV)
0.75
0.19<HK0.28CeV'
5
2.5
0
1 0.75 tM.„. (GeV) M.„. (GeV)
6
-U_L
0.75 1M.„.(GeV)
0.75 1M.„_ (GeV)
-2
O.2ß<lll<0.5 CeV
0.75 1M.«.(GeV)
Fignre 9.5: The dilfcrcntial cruss scction ii(T/tfM,tf- in dilfrrcnt |^| bins. Thc poinls rcp-rcscnt llic data and t ho cnrvcs imlicatc tlic icsnlt of tlir- Ml accordiiiR tu pqnalinn (9.7)Tlic daslic-d tnrvp rcprrscnts tlic ItUrd resoiMiit cnnt.riljiitiim, tlif dnt-daslicd rmvc tlic 11011-rcsoiuinl cotitrihution and llic ddttoci uurvc thc conlrilmtioti rnim tlic intcrfcrcuc-c UTIII. Thc
tnrvr is ttic suni. Onlv thr stnti.stical crrors nrc- shmvn.
thc (irst P* liin to ~ H! 6 in tlic Inst hin. Tliis ncgli^ihlc ilorrcasc nf Q1 can nol n-sult in aroiisidcritblc chmigc of tlic anionnt of skoving. Tlu'rcforL1 Ihi- olist-rval dcrrcasc of skcwingäs a fnnctioii of |(| is not duc to a convohilmn of rffnrts duc to |(| and Q2.
As is evident. Froni fignrc 9.7, thc Söding niodcl calc nlation of Ryskin and Sliahclski (fülltinc) is ablc todcscribc thc data, aflcr cvaluttMng tlm frcc parmwlcr of thc niudct (a"p) fronillic diita. Ou thc otlicr hand figurc 9.7 shows that t In* ainontit of skcwing is biggcr ihancxpcrtcd in tlic- ROSS Stodolskv niodcl {cquittion (99)), wliicli prcdicts a inaxiniiini valuc ofn = 4. Also thc final statc inlcractioti niodcl (dashcil linc), äs givcii by c<|iiation (911) , is
1(11
^~. t
vs09
m 08
0.7
0.6
0.5
0-4
03
02
|T
i n« i\ n \ * n f.
Fignrc 9.fi: The ralio \D/A\s a fiinction of |(| otilaim-d by fitting cquation (9.7) to thc
data. Thc inner rrror bars indicatc thc statistical crror, thc outcr onos thc statistical and
systnnatic crror addrd in quadraturc.
• Ihisonolyjis •O Clodditiqeloi. (E, - 2.9-4.7 C«V)
OGA Bollom ei öl. (E,- 2.8.4.7 ond 9.3 GeV)
0.1 0.2 0.3 0.4 0.5Hl (GeV)
Figuro 9.7: Tlic pnramotrr « äs a fiinction uf |'| (solid points). ftcstilts of fixcd targfl
rxpcriinciils |9Jj, J7] arr also sliown. Thc füll lim- indicatcs tlic rrsult of a Sciding niodcl
calculalion and thc ilashcil linc tlic prcHiction of Ihc final statt1 interne!mn rnotlcl (9.H)
'J.3. St mir /irf;ui,-ui( Mnsx HI:
atiiniint of skrwing nor t In- \t\c of tlic skrwing paranu-tfr n. In this niodrl n = 4
i,s cxprctt'd für l = 0, whcrcas thc rla^a indiratcs a riuieh tiiggcr vnbic (»f n(( — 0) ~ G.
Thc vahics oblaincd for \D/A\d n in bins of |/| arc snniinari^cd in Appendix C, togelhcr
with thc systcinntic mors from all crror ulasscs afft'cting Iht- rcsult.s.
At low energirs it was fonnd (hat thc u» nicson has a stnnll ainplitudc to dccay into TT^TT".
This ainplitudc intcrfcrw witli thc pn prodiictton ampliludc, \vhith Irads to a distortioa of
thc jr*jr~ niass sprctruni at thc w mass (/U„. =781.9 McV). To scc, if this cffcct can changc
thc rcsults dc-rivcd abovp, thc following prcscription incliiding p - u intcrfcrcncc was fittcd
to thc data:
BA.
- K f y2
(9.12)
This prcscription is an cxtcnsion ofequHlion (9.7), in wliidi t IIP p° propagator is rrplaccd by
a suni of t wo tcrnis. Tlic first one describcs p° produrtjon ;ind tlic second one u; prodnction in
thc 7r + 7r~ cliainu'l Tlic paramctcrs C and n drscribc ihr relative niagnitwlc and tho relativephases of thc ijj und p® trrtns. i\fu and T& arc tlic niass ;nnl ihc width itf tho o; nu-son. Due
to tlif vary narrow width of thc u nicsoii (F , = 8.<1 MrV) this study was pcrforniccl in a vcry
finc liinning (bin width: C.25 MrV) usuig corrrL-tion mctliod (b), in wliirli thp rcsolntion was
takcn into account by a convolution of cqnatJon (9.12) with a CJaiissi.tn rrsotiitton fimctioti
(swtioii C.2). Tu gt't rid of slatistical Ilutituations coining frorn tho accfplancc corrcutiun,
0.85.„_ (GeV)
Figurc 9.8: The- corrcctcd niass distribntion in ihr niass ränge 71)0 < Ä/„ t w - < 850 McV
analyzcd using corrcclion mctliod (b). Thc dasln'd linc shows thc rcsult of tlic fit according
to cquafion (9.12) «'ith ( sct to /cro (nn p ~ u; intcrfcrcncc) Thc fnll linr shows tlic rusult,
if < is Ircatcd äs a frcc paranictrr in thc fit thns iillmving for p - u> inlcrfcrcncc. Thc crrorsiirr Ihr ütatistical cnors unlv.
Parameter
AV (M<-V)r0 (NU-v)
' (,,b)fl//l (GcV-1/1)
AC (McVJ
co (dcg)
X'/'VDF
no p — u.'intcrfercncc
773 ± 1158 ± 1
7.43 ± O.OG
-0.758 ± (1.015
00 (fixH)
83.8/7G
with p — (Jintcrfcrence773 (fixrd)158 (fixrd)
7.51 ± 0-05-0.742 ± 0.008
788 ± 20.005 ± 0.001
99 ± 1271.9/75
Table 9.3: IlesuKs for tlio fils accordmg to cqiialion (9.12). The crrors an* tlu1 statislicalcrrors only.
the acrcptance «, wns fittcd liy 11 sccond ordcr polynomial and thc acceptancc corrcction incarli M„t„- bin was calculatcd by this function. Tlic stndy was rcstrictcd lo thc mass rängeIhr 500 < A/...- < 1000 MrV. In fignrc 9-8 thc corrcctcd mass distribmion in ihr limilcdrnnss ränge 700 < Hf,*w- < 850 McV is sliown, in wliicli p - u> hitcrfcrence sliould sliow up.Tlir vahic of Ars '" »M tnc fils acrording to equntion (9.12) was fixed to tlic valuc givrnin (ahlr 9.1. Tlic fit was performcd in t wo strps. First a fit was made in which C was S(>t
to zcro (no p - u) interfercnce). Thc rcsult of tliis fit is sliown äs thc dashed linc in figtire9.8. Aftcrwards a second fit according to eqiiation (9.12) was pcrfornicd, fixing the massand t In- widtli of llic p° to the vabics obtaincd in thc first fit. Sincc thc mass resolutionin th is stndy (=s 7 MeV) is of ihc oidcr of thc width nf thc u; mcson, it wontd bc dimciillto determine Fw from thc fit ofcquation (9.12) Thcreforc I\ was fixcd to thc PDG vabic(F^. = 8.4 McV). Thc rcsult of thc sccond fit is shown ns thc füll linc in fignrc 9.8. Thisfit is ahlc to dcscribc thc data in llic rcginn of thc uj mass. Onlsidc thc w rcsonancc rcgionthc t wo ciirvcs coincidc. The parametcrs dcrived from ihc two fits arc summamcd in tablc93. Thc \INDF improvcs from 83.8/7G to 71.9/75, if p - w intcrfcrrncc is includcd inthc f i t . Thc result of thc fit für thc w mass is higher than thc PDG valuc of Mu = 781.9± 0 l McV and thc relative niagnitndc and phase wprc found to he (, = 0.005 ± 0.0()1 and(t = 99° ± 12°. Changing thc mass resolution in thc fits by ± 25% changcs thc h'lrcstiltsfm ( by ± 0.002 and for a by ± 3". Thc niagnitiidc is smallcr lhan lhat mcasnrcd at lowcrcncrgics (( = 0,01 for H71P <, 4.5 GcV), whcrcus thc phasc is in agrccmcnl wi th prcvionsincasnrcmcnts (n ss 100°) [10].
Thc vahics of A* and D/A do not changc signifitanlly whcn p - u; intcrfcrcnrc was includcdin Ihc (it. Thns thc effcct of this iTiterfcreiR-c phcnonicna on ttie rcsnlts dcrived abovc isiic-gligihlc.
9.4 The Elastic f Photoproduction Cross Section
In Ihr prcvioiis scction diffcrcnt mass prrsrriplinns wrrc fittcd to ihc diffcrcnt i i i l cross sc-ctinndn/iiM„t,-. In this section thc clastic f>° photoprodurtion cross scction wi l l bc cxt rac t fdfrom tlicsc fits Sincc thc cross section dcpcnds on thc proccdnrc nscd to cxtracl thc rcsonanlpari from ihc mass d is t r ibnl ion , in this analysis thc following tfchniqiics of dc t r rmi r i ing thc
'j.!._ 7'Jtc f'jatjic /'' f ' )n»t(»jtun/m'f fön C'tuss Stt'tion
p" ITÜSS scction wcrc nscd and coniparcd:. e
• Thc Söding modd cross section. In thc Söding nuxlcl Ihc rcsonanl /in cross scction isproportional to thc ,irca of thc Brcit-\Vigncr cnrv«, tlint is the arca nndcr t l ic daslicdcurvc in fignrc 9.1. The arca was obtaincd by integraling thc Drcit-Wigncr fui ict ionninltiplicd by thc nonnatixntion paramctcr äs dctcrniincd by thc fit (,4! in equntion(9.7), A0 in cquation (9.8)). In this analysis iwo diffcrcnt paramctcri/aiions accordinglo thc Söding modcl wcrc considcrcd (Standard Södmi/cqiiation (9.7) and Spital YrnnieSöding pquation (9.8)). The valncs of A/p» and F0 uscd in thc Integration of the Drcit-\Vigncr fnnction arc thosc givcn in (ablc 9.1. Thc Scxling modcl cross section givenin thc following was detcniiincd «sing thc H t rcsnlts uf thc Standard Södini) fit. Thediffcrcncc in thc cross scction, obtaincd «Fing thc filrcsnlts of thc Standard Södint) andt ho Spital Ycnnie Söding fit, was incltidcd in thc systcmatic crror. This systematicerror can bc regarclcd äs an cstimatc of thc crror dur to nnccrtainlics in thc Siklingmodcl. Thc Integration limits nscd for thc integration will bc discusscd bclow.
• Thc parametrrization cro.$x tection in this proccdnrc thc cross scction is givcn bythc integral ovcr thc rcsonant pari of thc linss Slodolsky prcscription, naincly thcintegral ovcr f t p D \ V ( M 1 l t f - ) ( ^ f l f , / ! ( f , t , - ) ' t . Thc pannnctcis ;Upo and F0 wcrc thoscäs dctermincd from thc fits according lo er|iin!ion (9.10) (labte 9.1} In this approachall i r^n" pairs, othcr lhan thc oncs originating froin the backgromid givrn by ft><;, arcconsidcrcd äs coming from cliistic /'" photoproduction. Thc same intcgralion limit äsfor thc Söding model cross srction wcre usctl.
• Thc phenomrnologiral Södmq modfl c.ross scr.tion. This cross scction was cxtractcdfrom the invariant mass distribntions by a proccdnrc snggcstcd by Spital and Yennic[102]. Spital and Ycnnie argucd that in thc Süding modcl, thc non-rcsonani barkgrotmdhas thc property of going to zero at thc p0 mass. Thns thcy have suggcstcd that thcp° cross scction bc dcfincd äs:
71 Fn(9.13)
whcrc the p° mass fl/^o and width FO arc takcn from extcnial sonrccs, smh äs collidingbcam mciisurcments. Thc rccommciulcd proccdnre is lo mcasurc thc wholc spcctrum,fit it appropriatcly, and nsc thc fit to delcrminc thc cross scction at thc pn mass. Inthc prcscnt analysis, thc plirnomcnologiral Söding modrl cross srclion was dctcnnincdwith filpa = 770 McV and FO = l ."i") McV and nsing thc rcsnlt of thc fit acrording tocqiiation (9.10) Thc valncs for KIp and F0 are thusc, choscn by flauer et al. [10].Using thc same values for M„n and F0 is csscntial in ortler to comparc thc rcsults fromdirfcrcnl cxpcrimcnts.
Thc integrals in the dctcrmination of thc Söding modrl cross srction nnd thc paramrterizalioncross srction wcrc carricd ont in the ränge 2Af, < A/ .»,- < M„o 4 5Fo, whcrc tlic /i° massand wid lh wcrc takcn from thc dihVrciil fils respcctivcly (tablc 9.1) nnd A f. is Ihc pion mass.Thc intcgrntion rcquircs an cxtrapolation bcyond thc mcasured ränge. The nppcr l imit ofthc Integration ränge approximatdy correspomls to thc mass of thc ncarcst rcsonancc, thcp'( 1-15(1), with ihc sanie quantum riiimbcts and qiuirk contcnt äs the p11, ( l ianging thc iippcr
KI8
Söiiiini 'iHxli't citisa fft.tum (9.7)
{||',P) (GcV|
71.7
5-1.8
64.9
749
89.G
a
fjip-'f v (ft\t) for rorrcction
iiictlioil (a)
11.27 ±0 .16Ü ?,f
in. 90 ±o.2i!!.J|
10. 7G ± 0.21t] H
11.39 ±0.2G!|.?}
1 1 .67 i 0 2G_| ]•)
0.157 ± 0.059+.J} [JJ
gip-'fp j ^ j j j for rorrrction
nictliod (b)
1 1 .37 ± 0. 1?!] jj
10.88 ± 0.21t] 29
10.67 ±0 .19 t ] f3
11.15 ±0.22tS; ]^
11.46 i0 .22 t j^
n iofi -i- nn^ji"*"^1^
parometcrizatinji croaf seftion (3.10)
( 1-K.) (Gc )
71.7
54.8
64.9
74.9
89. G
a
OIP-*P p (jt|,j for rorrcction
nictliod (a)
12.63 ±0.18!| H
12 20 ± 0.24t! .5?
12.06 ± 0.24!!;iS
12.77 ±fl.29!|-y
13.11 ± 0.32t! IS
0.162 ±O.Ofil!jJ i!S!
(j-rp-*/1 p (j(]() for corrcction
nictliod (b)
12.85 ± 0.19t]Ji
12.29 ± 0.24t] 11
12.11 ± 0.24t] je
12.78 ± 0.25t! «
1306 ± 0.31t!??
0.142 ± 0.059tSÜo
phenomcnolt>gii-nl_StHliiig_itHMt?l rrow scchon (9.1.1)
(Wv,) (GcV)
71.7
54.8
64.9
74.9
89.6
a
p-rp-'p P ^,),j fot rorrcrtioii
nictliod (a)
13.72 ± 0.19t] "
13.25 ± 026t]"
13.10 ± fl 26triB
1387 ±0.31!]^
14.24 ± 0.35!, jg
0 162 ± O . M 1 !jjg
ff-'f-'p P (;,h) for rorrertionmcthod ( l > )
12.91 ± 0 .19+j ]J
12.35 ± 0.2-1
12.17 ± 0.24
1 2 8 5 ±0.25
1 3 . 1 2 ± 0.31
-1 50
-1»
*i n-1 .43
+ 1 14-1 41
0. 142 ± 0.059_o ]4g
Tnlilo 9/1: Tlic intcgralcd cross section <r """*'' v for t wo eorrcrlion metliods and thc dif fcrcnt
cx l ra r t ion proccdurcs. Tlir valncs fnr thc SÖduiq model cross .trclion atid thc pornmrd'n'za-
(ii)H rro.fs scrtion arr givcn for Mio rnngn 2;W, < A / . i » - < A/p» 4 5P0. All crnss scrtiDiis are
olilaini 'd fnr \t\ 0.5 G»'\". The lioltoin l inr of ('iich Inh lc slmws l l i r r t -sul ts uf lils to tlio
dala w i t h a f u n c t t u n of thr type H'"
D.I. T/n- Elaalic /'" Cioss IU9
l i i n i t lias ;i ncgligililc clk'i't cm t hc pnj'njrirfm'znd'on rro.'i.'i .wtwii, wlicroas t In*
Siiihnf) viodrl cross ftr.lion tli;ingrs (^msklcialily. For cxniTi|>k', if t l ic inlcgial is compuLcd
np to jl^u + 4F0, Uic Södinfj modii rross acftion di-crcascs hy 3%. If instcad tlu- ii|>|)cr
l in i i l is rxti'iidrd to Mpo + GF0 it incrcasi-s liy 2%. ()n t ho othcr l inni] tlif pornnM-ipnzaiioH
crosi .'iiT(io;i cliangcs Ijy tt-ss than l°/oo für ihr Siinit cliangr of Lhc iippt-r intcgralion l i in i t .
Thc rrasoii of this (Icpi'ndriire of thi* So ding modrl cro.ts trction on thc intcgration l iu t i t is
ol)vioiis front figurc 9.1. For niasscs aljovi- thc p° inass thc Dn'it-\\'igncrcurvc (dashc*! ciirvc),
rcprcsrnting thc rcsonant prodnction, is abovc tlir data aiid rompcnsatcd liy a negative
inlcrfcrciicc cnntri l iution (dottcd curvc). Tlic rpwmant n m t r i l > n t k > n is tlius still siwablo
cvcn for tnassrs ahovc 1.2 GcV, ivlicn1 Ihc nirasurcd CTOSS scclion is qnitc s inal l . For thc
paramctcrization cross sec.twn all pion pairs in » givc» inass rrgion urc consiilcrcd äs (P
productinti. Duc lo tlicskcwing crTcct tlic dilfcrcntial cross scttion do/rlM„i,- dccrcascs vt-ry
qu i rk ly for inrrcasing inass and thcrcforc tlic parametnization crufs srr.tion is itisrnsitivc to
tlic uppcr intcgralion l i in i t .
fn loiv cncrgy pliotoprodiiction cxpcrinirnts thc Södmt) tnndrl rrms srctwn was dctcrtniticd
liy ;in intcgration of thc Drcrl-Wignrr mrvc OMT thc avaihhlc ptiasr s|);ttc. At HERA
rncrgics this would rcsidt in a vcry riig nppci in tcgrat ton liniil iitid duc to Uic Söding cf-fctt (positive Brcit-Wigncr is cunipcnsatcd by a negative intcrfcrcnrc conlribiition at high
massps) this would load to a big contribution tu (ho cross scction from tlic mass rcgion almvc.thc nicasiircincnt. It srcins qncstionabk- to apply thc Söding modrl for niasscs nmcli biggcr
tlian thc p° mass. Tlicrcforc an uppcr Integration l i n i t t of d/^i + 5Fn is a rcasonablc clinicc
for Ihc uppcr Integration l inii t .
In scction 9.3 thc invariant mass dis t r ibnt ion ivas studicd in foiir \\'-,v bins. Two diffcrcnt
corrrction mcthnds wert* uscd in thc analysis. Thc intcgratcd ~>p —> />°p cross srclion for
|/| < 0.5 GcV2 is sliown in tablc 9.4 For tlic twu corn'ctioti nictlmds and Ihc Mircc dif fcrcnl
proccdnrcs of t l ic cross scction cxlraction. Tlic cross scction is givcn fur thc wholc sample
and thc four \\\ bins. The rcsnlts oblaincd for tlu- t\vo corrcrtion inctliods arc in piod
agrecTiirnt for tlic SÖding modcl cross swtioJi and tlie ]mramdr.mation rrox.v srrtiott, wlicrcas
thc php.nomeiiological Södinij modrl crosa stvtwn shmvs diffcrcnccs of 8% in all H'1P. This
dilfrrcncc is duc to tlic d i f fcrenl way Ihc mass rcsolnüon is trcatcd in t l ic t\vo eorrcclion
mctliods. Trcating tlic rcsi»lntion in thc fit fnncl ion, rcsnlts in n lowcr valnc of <ln/dHf,t ,-
at M„t,- = A/p" and thns in a lowcr phmwmrnohfliral Södtnij modrl cr-o.w xcr.tinn. Thc
cross scction dcpends strongly on thc cxtnu.'tion proccdnrc. Thc Söding modrl c.ros.i srcl-ion
is thc smallcst, fullowcd by pammrttrization rross arctwn nnd thc plic.nomf.noliHiiral Södinij
modrl rross sc.ction. Tlic syslcinalic iinccrlainty is dominatcd by Ihc i incci la in ty on thc
RCAL triggcr corrcction (systematic chccks 7 and 8) and tlic pmton dissociativc bnckground
siilitraction (systcmatic chccks 3 and 4) In tab lc9 "i thc typical systematic unccrtiiinlics, duc
to Ihc diffcrcnt crror classcs, ;irc summari/cd. Two of tl ic c i tor i'lasscs show a dcpcn<lcnrc on
H'1P, iiarm-ly tlic RCAL triggcr corrcction and tlic t rarking systcmalic. Thc total systematic
crror is on thc ordcr of 10-15%.
Thc cross scction mcasiired in tlic fo'ir H'1P bins was fit led w i l h a fnnct ion of thc type H'a .
Thc valiir of a oblaincd for tlie diffcrcnt corrcction inctliods and cxtraclion proccdures is also
givcn in tablc 9.4. Thc syslcmatic inicertainly of n was dctcrmincd by repeating tlic lit to thc
cross scclion valnes sliifted by a systcmalic check. Ttic systematic cnor classcs i to xii wert
considcrcd and tlic total syslcmatk crror was c;dcnlaled äs tlic qnadra t ic sum, ovcr all crrorrlasscs, of Ihc biggcst positive and negative dilfcrctices from the minimal rcsnlt in cacti class.
lil
cnntiibntion fromcrror class icrror class iicrror class iiicrror class ivcrror class vcrror class v icrror ctnss vücrror class ixcrror class xerror class xierror class xii (niclhuH (b) only)rnodcl unccrtiiinty (Söding inodrl onlyluniinosityradiativc corrcction
typica] niiccrtainly2-4%8-3%
4-10%1%
1.5%< 1%1.5%1%
0.5%1.5%0.5%4%
1.0%2%
Tablc 9.5: Typical inclividnal contributioiis to thc systcmalic unrcrtainty on thc inlegratcdITOSS scction.
Tlic error i:lass i (tracking systcmatic) was not consklcrcd in the total systcmatic crror of n,sincr the tightcr tracking cuts (systcmalic check 2) rc^ull in cross section valucs conipatibleivilh the nominal onrs, bnt willi statistical crrors in thc highcst U'1p bins incrcascd by tip toa faclor of t\vo. This incrcasc is diie to thc fad llial inost of thc tracks for high H'1P havcvcry small T/. Thc biggcr statistical crror on thc cross scction for systcmatic check 2 thiisicHerts Ihc cffcct that many cvcnts an- rcjrcied by tlic tightcr |n| cut. Thc biggrr statisticaleiror nt high \\\ niakcs it nnpossible to fit tlic U'1p dcpcndcncc of Ihr cross scction, sinccIhr (wo Iow Il',p bins dominatc tlic dctcrniination of n complctcly and ihcsc two bins alonchavc a too small Icver arm in H'1P. It shonld bc nolcil thal systcmatic chrck l (nu trackingcuts} results in valucs of a compatiblc witli tho nominal oncs. Thc uncrrtainty oti thcRCAL triggcr rfficicncy (crror class iii) yiclds tlic biggcst contribution to thc systcmnüccrror of n The rcmatning contribiitions to thc systcmatic crror of n arc gtvcn by thc crrorclass vü {changing thc fixcd valucs in thc mass fits insidc thcir crrors), ihr crrur class ix(dccrciising thc fit ränge), thc crror class xii (changing thc rcsolntion assumcd in corrcctionmi'thod (b)) and thc Sckling niodcl unccrtainly. All thc olhcr crror classes considcrcd in thcdctenninalion of thc cross scclion in H'lp bins arc conclatcd and thiis thcy do not conlributcIi» tlic systcmatic crror of a.
Thr cross scctions in thc fonr U"1P bins and l he slopcs n for all systcmatic chccks, affectingIhc rcsulls, nrc givcn in Appendix C'.
Thc valnc of a obtaincd for thc diffcrcnt protcdnrcs of cxtrarling tlic cross scclion and thclivo concction nicthods aro all con.sistcnl witli thc value cxpcctcd for a soft Pomeron, whcrcn äs 0.22 c.g.|37).
In ligiirc 9.9 and 9.10 thc cross scctions äs dclmnincd by corrcction rncthod (b) for Ihr dilfcr-cnt cxtraction proccdnrcs arc comparcd to a partial nunpilation of Iow cncrgy mcasiircnicnlsand rccciit ZEUS [l 10] and Hl [51| rcsiilts. The inner crror bars in figurc 9.9 rcprcscnl thc{jiiadralic sinn of thc statislical and thc iincorrclatcd systcmalic crntrs (tracking systcmatirsnnd RCAL triggcr e(ficicncy) and thc ontcr crror bars arc thc n,uadratic snm of staiistical
'J. l- : // l'Iiiiliipu.ifliii'tiiiii C'toss Si'i'l 111
and systcmatic crrors. In all thc plots those nicasnrrnicnts wcrc includcd, which usc thcsamc cxlraction proccdnrc. In h'gtirc §.9 thc Södinij madcl rross xrction is also conipared toa pnranictcri^atinn based on ücggc thcory whirh awumcs thc valnc of thc Pomeron intcrccptO|-(U) fbnnrl by Donnachic and Landshoffand by Cudcll et al., äs introdnccd in scction 3.3.3(scc fignrc 3.'l) rcspcctivcly. Thc parainctcri/ations \vcrc normali/ed to thc cross scctionnieasnrcd in [42, 80|, which wcrc cxtractcd ivith thc Söcling procetlnrc and (hcrcforc thccurvcs arc just inchidctl in figurc 9.9. AcluaMy thc atithor of [12j claimcd to havc uscd thc
-35OQ.t 30ü.
V 25
20
15
10
5
0
VOM & Pomeron (Cude» et öl.)
VOM & Pomeron (DL)
o Iow cnergy dato
* ZEUS 1993
* H1 1993
* this onalysis
(GeV)
Figurc 99: Thc inlcgratcd Södmg modcl cross sectton (r"""*1' ' äs a fniiction of thc ccntcrof mass eiicrgy H'„, Thc results of this analysis wcrc dctcrmiiicd witli concc-tion mcthod(b) anri are givcn for thc ränge 2;U, < Af,.,- < M^ + ör0 and \t\ 0.5 GcV2 Thcinner ciror bars on thc points of this analysis reprcscnt thc <|iiadratic simi of thc statisticalnnd thc tincorrelalrd systcmatic crrors and thc ontcr crror bars arc ihc (juatlnitic snm ofstatistical and systcmatic crrors. Othcr H ER. A rcsulls and a rumpilatinn of Iow cncrgy data[13, 104,81, 95, <17, 1(13, 42,80, 110, 51] arc also shown. Th<-rontinnons and dashcd linc arcparanictrri/atimis liascd on Rc-ggc thcory which assimic thc valnc of thc. Pomeron inlcrccptfonnd by Donnachic and Landshoff and by Cndcll et al. iTspectivcly.
Spit j i l aml Yriinie prun'dnrc (cr | i i i i t ion (9.11)), bnl llicy nscd (hcir iiifasnrrd vahics for the/i° niass and wid th i» cqnation (9.13) and tlnis (In- rcsult is cquivalent to an Integration oft In- Rrril-Wigncr curvc. It can bc sccn in figurc 9.9 thal a Pomcron inlerccpt of 0|.(ü) =l.1)90 (dashcd ciirvc in Hguro 9.9) niccly describcs llio Hata above 9 GcV in U',p. Thr sys-teiiiatir crror of tlic data prcscntcd in this analysis is on thc other liand still too big to allowa discnmination bctwcen dilfcrcnt ni-(O) values. H shotild bc also kcpt in mind tltat thcabsolute normali/ation üf tlic cross seclion dcpcnds on thr dctails of the procedure used tocxtract thr cross scetion froni tlic mass distr ibution. Thcrcfore. it secms to bc rcasonablc todctcrii i inc f*r(0) froni clastic f>° production in one cxpcriiiicnt instcad of coniparingdiffcrctitmcasurcmcnts. The nieasurcmcnt presnitcd in th is thcsis docs not allow to dctcrniinc O|-(0)
-^ tu
^ 30<X'Q. 25
| 20
'b' 1°5
• — •• — * oOQ.'Q. 25
f 20Q- 15r*«
V 1°5
° Iow energy do• E665• Hl 1993• this anolysis
^üi[OgWf
*° o O % • •" ! * * *
-
10 io2 wff»
. o Iow energy dor || • this onolysis
- iV
& o o # » * »" o
'• , ,
10 to2 w
ta
(GeV)
ta
CfioV^
Fignrc 9.10: Tlic intrgrntrd pnrnmetenzation cross scctioii (uppcr plot) and thc jiliennmr.no-lofjicnl Söding mottet r.ro.ts scction (lowcr plot) o'*f~tf " RS n function of tlic ccntcr of mnsscticrRy H'^p. Thc rrsults uf t l i i s analysis wcrc dctcrniincd wilh corrcction nicthoil (b) and arcgivcn for tlic ränge \t\ 0.5 GcV2 and IM, < M,*,- < A/^o + 5P0 for thc parainctcrizationrross scction. Low energy dala olitained will] thc sanic cxtraction procedurc arc also shown.In thc uppcr plot nirasurenicnts by (104, 95, 103, 80, 5l, 39] wcrc includcd in Ihc plot andin thc lowcr plot incnsnrcnients by [75, 104, 81, 95, 80).
y.,r) 'Mir' 113
prt'cisi-ly, since tlic Icvcr arm in M"1p is s inal l .
As can bcscen froni cquation (9.13) the phetwtnrnolflQit'nl Södmq Jiiodi-l rross scrtion dcpcndslinrarly on ttic valnc of P0 uscd. A valiie of r0 - lä'j McV was snggcstcd by Dauer et al.[10]. Him-evcr thc latcst valuc of FQ froni vaiious rcnctions cxn-pt pliotoproduclion, givcnin Ihc PDG, is P0 = 151.9 McV |82|. Using tliis smaller valuc for Tn slnfts all points in tliclowcr plot of figurc 9.10 downwards by 2%.
Thc rcsults prcsrnlcd are eonipatible w i t h , bnt systmuilically hiwrr than tlmsc presenlcd in(110). Tlic rcason is twufold. Tlic protun dissociativc Imckgronnd dctcrmiiH-d in this analysiswith thc usc of the LPS (scction 7.4) is largcr than thc 1993 cstimatc. Thc RCAL triggcrcfficicncy has bccn dctcrniincd froni data in this analysis (scction G. 1.1) and is approxinmtely10-20% higher than that cstimatcd in (l 10].
9.5 The \t\n
Thc diffcrcntial cross scction ila/d\t\s obtaincd by lirsl ca lmlat i i ig thc di l ferential crossscction da/dP*- and aftcnvards applying thc corrcrtion f in i c t inn F (cqnntion (4.8)}. Ascxplaincd in scction 4.2 thc fiuictiuii F accounts for t l i c r l i f fcrc iuc betwccn Pf- and |/| ducto the non-^cro (J2. Thc diffcrcntial cross sct-tion rfn/rf|/| was dctcrmincd for all events intlie niass rcgion 0.55 < A/,*.- < 1.2 GcV and in eighl bins of / U „ + „ - . Thc bins arc givcn intablc 9.6. Thc funct ion F was calculalcd for thc wholc niass ränge and in thc cight niass binsseparatcly. Thc corrcctcd diffcrcntiat cross scction nblained in this way is shown in figurc9.11 by thc fnll (lots. Thc opcn dots in figurc 9.11 stmiv the diKcrcnlial cross scction dajd\i\d wi th the LPS. Fnr this measurement claslic events wcrc sclectcd using the LPS
(0.98 < z/. < 1.1)2). Thc variable |f| was nicasnrcd dirccllv by thc transvcrsc niomcntiiiiiof thc outgoing proton, nieasnrcd in thc LPS. Thc bigger slalistical error bars rcflcct (hesniallcr statistics availablc for this nicasurcrncnt. Thr LPS acrcplance is almost zrro bclow|f| of 0.08 GcV2. Thcrcfore thc LPS poinls are onlv shown for 0.08 < |/| < 0.5 GcV2.The rcsults obtaincd for the nntaggcd sample ( fü l l d"ts) and Ihc LPS sample (opcn dots)are in good Agreement. Thc agrccmcnt in thc absolute nonnali /at ion howevcr is t r iv ia l inthis analysis, siurc thc LPS taggcd events wcrc uscd to dcterniinr the amount of prutondissociativc background in thc nntaggcd sample (scclion 7.4). The- agrccmcnl on thc slopein | f | on thc othcr hand shows Ihat tlic procedurc used to cnncct (hc mcasured P'- to | ( j ,by thc corrcction function F, givos thc corrcct value i»f |/| A incasiircniciit of thc |/| slopc
lowcr l i i n i t11.550 GcVO.GC7 GcV0707 GcV0.735 GcVII. 757 GcV0.782 GcV0.815 GcV0.87 GcV
M,^,- bitisuppcr l i in i tO.GC7 GcV0.707 GcV0.735 GcV0.757 GcV0.782 GcV0.815 GcV0.870 Gc-V
1 .20 GrV
avcragrD . G 1 7 G r V0.088 GrV0.721 GcV0.74G GoV0 7G9 GcV0.797 GcV0 8,18 G<-V0951 GcV
Tablc 9.G: A/, t « - bins uscd in thc stud\f die |/| distr ibi i l iun.
0.1 02 0.3 0.4 0.5
Itl (GeV1)
9.11: The differnitial cross scclinn dajd\l\r llic proccss 7;) -+ 7r + 7r'p in tlic kino-niiilk- Mtigc 0.55 < /V,.,- < 1.2 GrV .nul 50 < \\\ < 100 GeV. Thc füll Hols sliow tlicrcsiilts olilaincd for thc wholc s;iinpk' am! tltr opm flols tlic rcsnlt for a siibsaiiiplr of Ihrfvciils in whirli tlic onlgoing proton «äs nu-asnrrd in tlic LPS. For tlic opcn flols |(| wasniriisiircd nsing tlic transvprsc niotiicnMitn of thc oiitgoing prolon äs nicasurcd l>y tlic LPS.Thi- (.'on t i n n i ms lim1 rcprescnts tlic rcsnlt o f thc fit \vitli tlic fmictional form (9.14) to ihc fnlldols Only stalisticiil rrrors aip slunvn.
nsing tlic LPS laggcd pvcnls is shown in |1I4|.
Tlic cniss scclion dajd\t\s an cxpnncntitil fall rlinractcristic of diffractivc proccsscs(scclion .1.3.2). As rilrcaily fonnd in hndronic itilcuictions tlic |/| distriltutJon can lic fittcd:
(9.14)
Thc littcd valncs arc b„ = 11.4 ± 0.3 stat *g J «yM. GcV-'aiH r„ = 2.8 ± 0.7 rtal. !J j syst.GcV-V
Fils aiTonlinR to cqualion (!).14) wcrc rcpcalcil in Ou- /U, + ,- liins. In Hgnrc 9.12 thcpanum-lcr r„ is shown äs a function of A/, + .-. No dcpriidcnt-c can bc SITU in ihr dala.Tlictcforr- in thc folloiving OH- valnc of r„ in Oic fits nccurding tn oqnalion (9.14) was fixcdto r,w = 2 8 Gi'V~V Fils according to i'qnation (!) 14) wcrc rcpcatcil in M,t,- liins and l IIPslopc parainctcr b., is shown in ligurc 9.13 äs a function of /U„t„-. Tlic stntislinil rrrors arc
^ 8
^ cO 6
0 4
0.6 0.8M.*.. (GeV)
Fignrc 9.12: The cnrvalnrr paramctcr r„, rcsidting from a fit of equation (D.H) in dilfercntinass liins fnr Ihe rcaclion -y)i —> n*"7r~p. Tbc kincmatic ränge t.s öl) < 1I'1P < HHI GeV and\t\ U.ü GeV2. The crror nrc slatistical crrors only. Tln- fnll l ine rcpresenls tlir rcsnlt ofOic fil for Oic whole snmplc and thc dashed lines it's stnttstical rrror.
0)Ü
15
12.5
10
7.5
0.6 0.8_ (GeV)
Fignrc 9.13: Thc slojic paramctcr b„ icsnlting from a fit of rqn;itioii (9.14) in diffcrcntinass liins for Oic rujiction T;I -> if*T\~p. Tlic kincmatic ningp is 50 < \\'-,p < 11KI GeV andt^| < II ö GcV2 Thc füll Hm1 rcprescnts ihc resnlt of a ralcnlation by Ryskin and Sliabclski(s<-c tcxl). Thc inner rrror hars inrlicnlc thc siatistiual nneertninty an<l thc- unler ones tlirstiilishcal and svslcniatie nnccrtaintirs snniined in qnadratnrc.
slmwn iis the inner ciror liiirs and llie outcr crror Kars rcprcsent tlic s ta t is l ical and systcmaticmors addcd in ij i i i i( lr; i t t irr . Thc rapid decrcasc nf h„ w i t l i ine.reasing mass is consistctit witl it l ic uliscrvation Ll i i i l Ihc atiionnl of skciving dccrcascs ;is a fnnction o f | f | (Irgnres 9.G nnd 9.7).In tlic fraincwork of gcornclric diffnictivc rnodels Mir decrcase of tlic slopc, indicatcs tliat llicradins of tlic ffp intcraction dccrcascs äs thc rnass oflhc pn incrcascs. Thc decrcasc of /•„ äs afunct ion of mass was alrcady obscrvcd inear l ier niciisnrenicnts [1,92, 28, 13, 1(14, 94, 95,80, 2]a i i f l is cxpcctcd in the Söding moilcl and in ihc f ina l statc intcraclion tnodcl. In figure. 9.13tlic prcdicHon of tlic Söding modcl calcnlation of Ryskin and Shabclski [88| is shown äs afu l l l inc. Tliis ciirvc was obtaincd äs discnsscd in ntorc dctail in srction 9.3. Thc curvc nicclyrcprodnccs l l ic data .
Tlic valucs otitaini'd for 6.» in Uns of iUm*„- aro snmmari/cd in Appendix C, togcthcr w i t l iihc systcmatic rrrors froni all crror classcs al'ccting ihr result.
Sincr thc amotint iif skcwing dccrcases äs a fnnct iun of |(|, t In* diffcrcntial cross scctiondo/d\f\r tlir rrsonanl procrss -yp -» p°p was dctcrmincd os follows. Mass fits ivcrr carricdout in hins nf P* using corrcction inctliod (a). Thc p° niass and width wcrr fixcH to tlit:valncs givcn in tal i lc 9.1. The rcsonant part of tho cross soction was cxtractcd äs a f i tnct ionof P7! äs cxplaincd in llic prrvious scction. All thn-c ox t rac tKin proccdnrcs wpre considprcd.Again tlir Södmfi wodc.l croas ncction was olitaincd frotn tlic fits of cqnation (9.7) and thcrcsnlts oblairicd front llic fits according to cqnation (98) is considcrcd äs an cstimatc ofthc systniiatic imrcrlainlv of tlic Söding inodcl. The di l fcrcnt ia l cross scction rfo/rfP72 wascorrcctcd to do/d\i\n by applving a corrcction function F.
Thc cross scction dnfd\t\d front thc rnass fits according to cqnation (9.7) is ploitodin lignrc 9.M and t l i c rrsult of tlic fit witli thc fiiriclmn
0.3 0.4 0.5
Itl (GeV2)
c 9.14: Thc diffcrcntial cross scclion dfl/d\t\r thc proccss ip -» ff p dctcrniincdfnnn ihc SridinQ model rross fi'c.tton in tl ic k incnia t ic ränge 2A/„ < ^ f * ^ , - < /U,,o + 5r0 5(1< H"-,,, < KHl Gc\ Tlic fontiimmis linc rrprrscnts tlic rcsult of thc fit wit l i thc fnnctionalform (9.15) to t.lic fn!l dots. Tlic statistical crrors arc sinallcr t l imi thc si« of thc syniliols.
9.5. Tlic
Söding modd
-V (/'VGcV)
1124 ± 2.5 tiV
r V (ov-2)10.88 ± (1.34 tu JJ
r,,.. (GeV-*)
2.70 i 0.91 Ü?l
paramc.tcrizatwn
•V (/'VGrV)
148.8 ± 3.4 !^i
V (Gi-V-a)
12.G1 ±0.34 tSS
V (GcY-<)
4.97 ± 0.89 tm
pkcnotncnologic.nl Söding modcl
-V (/ih/GeV)
140.9 ± 3.2 tu*
V (GeV3)
11.12 ± 0.34 to«
<V (Gc\-'}
2.99 ± 089 t{a?
Table 9.7: Rcsults of Ihr fits according lo cqnation (O.Ki), to Ihc diffcrcnlial cross scctiondo/d\l\r thc proccss i;> -> p°p. Thc rcsnlts arc givcn for all ihrcc i 'xtractinn procednrcsnscd in tliis analvsis.
_
d\t\)
is sirperimposcd. Tlic piiranictcrs olitaincd for t l ic d i l fc rn i l proirduri-s of cross scctioncxtraclion arc snnilTiari /fd in taltle 9.7. Tlic syslcniatic rrrors \vcic obti i iuwi by rcpcatingtlic wlmlc proccdnrc, whilc inclnding a systcmatic check. For llic Söiling niodc! thc positivesystcrnalic crror is l'iggcr than for thc othcr two proccdnn-s, sincr t In* diffcrcncc bctwccn llicrcsults obtaincd front Mir mass fits iiccording to cqnalion ( 9 7 ) aml (9.8) was considprcd äsan extra contribntion to Ihc systcmalics. For fy thc inntlcl depciiilcncc <if thc Sixling niodcljs Sbpt = O.C5 Gc\"2. The valucs for thc* slopcs b^ and r,,» are vcry s imit i i r for thc Södinginudcl proccdiirc and Mic Spital and Ycnnic rncthod, wlicrcas Mie paraiiicteri/,alioii crossscction givcs systcniatically higher valucs. Tliis diircrc'iic-e is cxpc'i'tcd, sincc for t l te Södingmodrl cross s»r(io» and t\w paramHrrizution rrofs fcction skcwing is trcatorl diffcrcnllv- Thcslopc paranictcr b^ ilcterinincd frnni thc parametenzatum <TO.S.< srrlinn is biggcr than bff
sincc llic lattcr was detcrniincd in tlie lintitcd niass ränge (l.").7» < A/„i , - < 1.2 GeV,
Finalty thc \t\n was stndied in difTcrent U',,, bins, Thc bin si/cs aro givcn in tablc92, ivhcrc tlic last [wo bins arc rwrgcd to nnc (70-100 GeV) Again niass lits wcrc porforrncdin Pf- bins. Afterwards a correction function F was applicd [n dctenninc da(d\t\. Thcfunction F was dctcrmincd for cach irw bin separatcly Figit ie 9.15 sliows thc dilfcrcntialcross SL'ction in tlir thrcc H'1p bins, obtaincd according ti» t l ic SiMÜng niodel procrdiirc,togcthcr witli thc rcsnlt of a fit according to cquatioii (9.1*)). For tlicse lits thc valuc of cpawas lixcd to thc valuc givcn in tablc 9.7.
In tablc 9.8 thc vatuos of bpo obtaincd for tlic dihYrcnl cross scrtinn definition.s arc givcnfor tlic thrcc 1I"TP bins Again thc biggcr positive svstemalic nror for tlic Söding rnndel isdiir to thc rnodcl unccr tHin ty , äs cstimatcd by thc diff i -rcncr bciwecri t l ic results obtainediising cqnation (9.7) and (9.8) ((iJy fe O.G GcV-'). In (ignrc 9.10 l.ltc So.ling inodcl resulti.s croni|»ared to an oMier rpc'Pitl rcsnll froui HEDA ( I l ( ) | and ;\n of Irm- cnc-rgy
1|IIS.»J .11)1 S,)|l!.)lplll .Il
""".11 J l > 1|O!PU||J B s'1!
,tllllHJpU[lt> UI [«HlUinS JIIJJJ .>lllMIJ.)]SAs
r>ipui i!]up s.132 '"H "° SJWl"l -lO-t-i-i Jlll '!Xl)J '''M u! p-'^insipljl .>!(.]_ "[(18 'i l' 'Hi 'Cl '62( |;'HP ASÜ.JIM A\0| JO Uolllqlduio:) B
i(] uf '«nijyjs sswj juputu Smpgg
M,0t
Ä&J3U3 MOJ 0
C661 S03Z 'S)SÄ|OUD S)
9901ZItn
o
(M
opIM ),
si '';u jo
j'o = ••« i\\\.\\) o
f)UK uojpunj
••',<> jo anjjo jiiiuiiiaisAs oip oj ^inc|iJiuuD 1011L( M oj Jau SUK| n u; »dq jo (io;ii!ii[iiu id|) oi(]'(s]ij ssüiu oi|] u; r|)|ii « )UJ|)UJi]jp uniiiuiuoui) ix syiij.i aoJJ.i puü (stioiinquisip s-;uiu 341 jo
.i) x üiqj JOJD A'I| u.Mi Jju '*u jn joJJJ ni)L'iu.)]SA!> oi|) oj suoi)iiqu)(ioj•,)! ui uii( oi iui{ LUO.IJ j jo uoiiuiipiiy jiionsimis oj oii|> 'jopmüjud 3>uj e su
(öl 6) uojpunj i; IJJIAI BH'l« j«.)s.)J£l Ji|| 01 si' s i s jA?uy yi i ) IM jsii s
'u aoj ä)|ns.u s.vioijs> Joj
n.i«jjo
oj o] joj s
ao+()2'u
TOß'ül
(r-A-'O)
SZ'O
T wziT 99'2I
T IC'ZI
(e-A-»0) (s-A-'O)
(e-A-'O)
6C8
01 i
siJI1Q
l ,)juii;.\jii3 .)i|) ji 'n jou,i/is ui )|iis.)J uu;i j jti
IHl J.1JJ l! SU |JO]B.IJ1 Sli.«
1011 Ü\i.\\A Üb1!|.l JOJJ.) Jl(J
^3oi|.i) sin, isi uosujJ Ji|) i ss«|j JQJJJ joj "'o jo
l-l JOJJJ Dj)BU|d1S.\
O] jij ai[i änqL'ori.jj Xqs aai{ -' o joj Ü,>H[KA
i 'j pui>
|L'iot Ji[] u; p.)piq.)in IGU OJ.H\A pui;O pOJJO JI{1 .tq [).)l(l|)
|j g g
uoiiBiilw) iiuoj üi(i jo ly y 'poj).) ^uipog ;>iji joj p.ip.ujo.i 1011 SUA
(91-6)
atp puW/A uoiiriqüisip j oi{i siii.>iiujnsi!Jiii osoip u; oouis 'üjriSy oip n; pjpnj.mi jou ,)JL*
.ii|l Sinsn s.13Z A"«l P"« [[?! IH AM "i *>Jols aiP J° siuoiu-uns^jv [(18 'lt 't6 tl '6t']
si l
1211
It <:;ui bcscen in ligtirc 9. l G t hat tlic incasurrd vahir für thcslopr of tlic Pumcroti (rajcrtory ufnj. = (l.23dcscriiics also pait of t In- Inwcncrgv data (dashcd linr in h'giirc9.lG). But it shonldl K- kcpt in mind tluit tlic valnc obtaincd for /y> dcpcnds un ihr dctails of thc proccdurc nscdtu extract thc cross scction froni thc niass (Hstribiilion. Thcrcfnrc it secrns to IM- rcasonablcto dctcrniini1 n't. in onc rxpcriiiicnt iiistcad of comparing diHcrcnt mcasiircmcnts.
Thc slopo bf» in tlic thrcc H'ir, bins and thc valucs of n\. for all systrmatic cticcks, alft-clingtlic rc-siilts, arc givcn in Appendix C.
9.6 Decay Angular Distribution
In Llic analysis of tmtaggcd p° photuproHnclion thc t wo anglcs ft, and tt>h in thc s-cliannclhclicity franic can bc mrasurcd Bcforr I)IP nngidar dislrihutions wert1 sludicd, tnass fitsaccording to cqttation (9.7) wcrc porfonnrd in c:ostfh and <f>h bins. Corrcction nifthod (a)
0.8
> 0.75OJO^ 0.7
S 0.65
0.6
0.55-1cos
5 0.03
^0.02
0.01
-
_
b 11
1 0cos 9h
Figure 917: A nimmt ofskcwing as measurcd by \D/A\d thc backgioimd coiitribiilinn .^,.sas a fuiirliun of tlic dccay angle cosö/^. Only slalislicnl crrors arc sliown. Thc hori^unlalcrror Imrs indicatc thc si/c of tlic bins
121
>0.75O
030.65
0.6
0.55£
r
'
—- W- 4 1 -TT~ t -t , t T— ,,— |-
i i i i i i> 1 2 3 4 5 6
<f>»
7
*«_-•
^0.02
0.01
0
-
-1 I , -|-
^ I ' T __Hh_— — „4 __._.._1 . . . 1 . . . . 1 . . : . 1 . . . . 1 . . . . 1 . . , 1
0 1 2 3 4 5 6
V*
Figure 9.18: Tlio ainounl of skciving äs iiicasnrrd by \DjA\d tlir bitckgi-ontid coritrilintionArs as « function of thc ilccay angle <bh, Only statistical crrors ;irc sliown Tlic horizontalcrror bars indicatc tlic si/c of thc bins.
was usctl and tlic p° niass and wiHtli WCTC fixer) to tlic valucsgircn in tablc D.I. Figurcs9.17and 9-18sho\ tlic ainounl ofskcwing, as mc-asurpfl by \D/A\, and ihc ainoiint ofbackgronndundor thc thc pn pcak as givcn by Ars ** fniirtion of cusft, and <f>lt. Tbc ainonnt of skcwingdous not sliow anv dcpcndctirc oti Ihc dccay anglcs. On thc nilirr band tlic backgronndcoiitribution int-rciiscs as jcus^J inrrcascs, but Ars is bi-low 0.03 in tlic wlmlr cos(?h ränge.No clcpcndcncc of Af, "» *« ''an hc s<rn in thc data. In surnniiuy thc inass sliapc docs notchnngc sigiiifitHiitly, as function of tlic decay anglcs. Thcrcforc in thc fullowing, tlic dccayangular distribntions contain üll cvcnts in tlic niass lange 0.5,") < jU..„- < 1.2 GcV. Nocorrcction für thc backgnnind was npplicd.
Thc tlrray angular distribntions of thc dccay pions allow to dclcrniinc Llif /»° spin ticnsitvniatrix clcinciits. As introdiiail in Kcctimi 3.34 tlic dcpcndcncc on cosflh and <f>,, can bcwrittcn as (rtjnation (3.72)):
12-2
After integratiriR over cos6h <>r $i, Ihu following onc dimensional distributions arc obtained:
3 f <H , <M Jfl l i-,
Tims (he spin dciisity matrix elcmcnts rJJJ and r^, can bc measured by fitling ihc twodimensional dislribiitinn (cquation (3.72)) or thc onc dimensional distributions {cquation(9.17} or (9.18)). Thc spin dnisity matrix elenient r{Jj} reprcscnls the probabilily that thcprudm-i-d p" nicson has hclicity 0. Thc clcmcnt rfl, nicasurcs thc intcrfrrcncc of hclicilynon-llip and double flip amplitiides, wliilc Srftj is rclated to thc intcrfcrcncc betwoen non-flipand hclicity singlc flip amplitiides As alrcady incntioncd in scction 3.3 4, if s-channcl
*•!
FiRiirc9.19: Differential dislrilnitions l/A'f/,V/f/cos9/, and l//WA'/d0/, for the rcaction yp ~*7r*7r~;i in thr kiiicinatic ränge .')() < iri(l < 100 GcV and | f j < 0.5 GoV?. Thc contitiuoits
rcprcsent tlic rcsulls uf the fit discussed in the Irxt. Only slatistical crrors arc showii.
'J.ti. 123
helicity nmscrvation (SCHC) holds. r°t, and flrft shonld In- /eru. In casc »f SCHC r°£is rclatcd to /?, the ratio of thc longitndinal to transversc cross seclton (n|iiatkiTi (3.71)).Siiice in thc kiiiematic ränge o f t he prcscnt data thc cruss scction for longitndinally polari/cdphotons is vcry small, r$ should bc small.
In figmr 9.19 thc one dimensional distribiilions arc sliown togcllier wilh the fits according tocquation (9.17) and (9.18). Thc valucs obtained for ihr spin dnisiiy inatrix clerneiits frumthc fits of tlic onc and two dimensional dimribntions arc sinmiiarJ/ed in tantc 9.9. Thc rcsultsobtained from thc two differcnt fits arc in agrccmcnt. For Ihc spin dnisity nmlrix clcmcnt^rio " positive valnc was fonnd, whcrcas rfl, tends to bc negative. Doth clemcnts arcvcry small and consistnit wilh zero instdc thc systcmatic crror. Thus thc data is consistcnt«ith s-channcl hclicity conscrvation. Assiiming s-channcl hclicity coiiRcr\'aiion thc measuredvaluc of r^o can bc uscd to cxtract thc paramctcr (,* in thc vcctur nirsoii dominance modctrclatron:
n = -=e$r. (3.19)
^ inscrtcnl in rt|iintiuii (5.0) yiclds f? =(I.22^J. Tlic avcrago t,)2 uf tlic data is (Q7) «0.01 GcV2. A valiic of f3 < l 0 is tonsislontwith low cmTgy clcctroproduction nicastircnicnts [4l, 27, 9, (>(), 29, 18, 21, 43, 39].
Tlic spin dfiisity matrix clnncnts r}Jo, !Rr°Q and rfl, arc also sindird äs fiinclion of |(| aiul/U,»,-. In thc prcscnt analysis |/| was not mrasurcd dircctly. Thus tlic ,spin dciisity nuitrixi-lrniciits wrrc mcasurcd in P7J hins and corrt-ctcd to |(| by mpiins of a Monte Qirlo Simulation.L'sing Monte Carlo cvrnts it was Fonnd, that the distritiiilioii of thc fingk1 ^, wliich ran notbc miMStirrd in tliis analysis äs well, is corrclatcd willi P\. Thcicforc tlic currcrtion for theros0n-0<j cli.stribution in |/[ bins dcpcnds (»n thr 't distribiition jissnmcd in thc Monte Carlo.In this analysis thc fy distrilnition was gcncratcd act'ording to s-channcl licliriiy conscrvatton(scrtion 5.3).
Tlic sine of thc Itins in |/| and il/,fF- arc givi'ii in tablcs 9.2 and 9.0. In fipiitr 9.2(t tlir spindfti.sity matrix clrnirnis arcshown äs a fnnction of |f|. Opcn ilots shuw tlic n-snlts oft In- fit tuthc two dimcn.sional distribntion and full dots thc rcsnlts olitaiiu'd froni thi' onc dinicnsionaldistribiitions. Statistical crrors aru indicated bv thi1 inner c.rror bars and thc nuler error bars
Rcsnlts of thc litsaccüiding to (9.17) and (9.18)
04roo
0.1)17 ±0.(W8!g S?J
04T l - l
-0.1112 ±IM)08!S SS?
Rfsttltsof thc fitticrording lo (3.72)
rw'oo
o.oii ± [i.onr+S.o??
flr04Ttr |0
0.012 ± ooor/o^
..0*' 1-1
-o.oio ± ».n(i8!!IS5J
Table 9-9: The valucs for llu1 spin dciisity matrix clcineiils nblained frnrn (Ms to thc decayangular distributiuns.
p;niiiiins H.
piiK (8I'(j) pm; (ice) s-iiijiti!iil>>) i'l äuipjio.H! üiy ,)i[i jo SJJHSJJ ;ii[i ju.is.i.id.ii SK
6'0 9'0 Z'O 9"0
i h i , '
(A»O) '""n-,—r 6'0 8'0 L'Q 9'0
6 * 4 i }n
^93) —*"H
6'0 S'O ^'0 9'0
* I H 1 + ^ -1 ^ I :
2'0-
ro-0
ro -,Z-Q l
Z-Q-
ro-
0
ro a-iZ'O 5f
Z'Q-
ro-0
ro7 -n St
UO^UUBA u ' tfl puu °^/yj joj p,»AJ.isqo JJJA\+*/v jo unipimj n SL- siu-nu-ip XIJILMU Ä)isujpiiids i>ip jo sräuuip [cßj iioi):>npnJdi>ioi|(.I A^JOIIJ A\O| u j -'"^.i uui( i j.iSäiq oq oj punoj SB.«
Sö-'ü Plll! " !s «ilis»J'lo >'AI;I[ 01 pojnstMiii OJB '~^.j puu ^jjfc 'jA°0 S'U > I'l JOJdi|}-uouoi|i ju<j^()2-cji j < i J jpjü.)[( j josjopnii |diue iliy MLI;|.>I{ .»p luqi puu aapniiidXq pDiuuiiuop si uopjupojd 0(y jiMp pOAJ.iaqo su.w ji ([g 'gg '09 'g '()l| Ü J uoipiipojdoj]M|,)Qd uj 'U^is iii a]isodi[o siii| .>pii] i[diuu di( j uuls ,>|qnop .->i|) si:>ujij\ '3pnii|duiL' dijj-uou ,n|i
SB u8is .liiius .ii[i sni[ äpti | i t( luiL> di|) inds 3[3uis ,»i|i ibij! piinnj SL-A\j ',^^0 (•'() !?| JOJse.» UOIHJAJ.WIMO A)i.ii | ,»i( {,»uiuip'S-jonopi:[Oi>\8 '96 'C6'Ul] '8 ' J J IIB JOJ
p.iimiiuinp yi iiDi).inpo.id-()(/ |i;ip puu x,ni.).\R ji(i )i> p.i.\jo«uo3 u
p-ü J.ijsnuj) iiiiiiiiJiuoiii KIMIIS tu n;ip jmiioj SÜA\i mup noipupojdoioijd A'Sj.in.i A«I| u j
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p Iow energy doia• ZEUS 93» ZEUS 94• Hl 94• Ihis anolysis
VOM & Pomeron (Cudell et öl.)VOM & Pomeron (DL)pQCD (Ryskin)
(GeV)
Fignrc !().!: Cross scction for vcctor mcsun prodnction in photoprucluctioii moasurcd byfixed target eN|icrininits arid the HERA cxpcriments ZEUS and Hl |19].
in thc. two UHR A cxperiinents and comparrs tlinn Ui nira.sincnH'iits at lowcr cncrgics. The(liffrrciicrs ticlwrrn ihr us and d> prodnctioii oltscrvrd ;it Irjw rnrrgir.s arc altrtbulrd to thofiict tlinl onlv PiirutToii fxfhangr nnitritnitt-s lo 0 proditciinn. Thcsr dilfcrcntcs arc abscnlin thr- HERA cncrgy rrgjon. The liglit vi-ttor incsuns slinw ;i wrak cnrrgy dcprndcnce,cx|)(Tlrd in inodrls basrd on VOM and Rcggc tlicory (sitft Poinrron). Tlic strong incrcascnf llic J/i!> phdtopmdnrtion cross sc-ctioti is inconsistnit «illi t In1 soTt Pomeron rnodcl, btitrmxlcls in ihr frjiiiii'wnrk of pcrtiirbativr QCD havo brcn ;ihlr to sncccssfiilly dcscribf thcphotuproductiidi nf J/iJi nicsons. Pcrturbativc c.itcnhtions ;irr applif.iblc in thp casp of Jj\l<plidtitprodtictiim sinco Ihc niass of llie -//i/> mrson providrs ttir lU'fcssary largc scalr. InQCD inspircd modcls Ihr inU'ractioli brtwccii tlir prolon nnd thc a" pair in Ihc pholoti isninlialcd by a glnon laddcr Thc strong incrrasc o f t In- .//v'1 uos,s si'clion äs a functioti nf H'1(1
is (lins rrlntcd tu thr risr- of tlir gluoii (iistrilmtion in thc protuti ;it stnall r. In (ignn- 10.) thr.//V1 mrasnrcmcnlK at HERA ['>3, 115) att- toniparcd \vitli tlir ic-sulls of [irrturbativc QCD
129
ralnilations for tlircc flilfi-rcnl gluon dnisitv i'iiniinclcir/iitions, whith rxliibil significalitlydiffcn-nl slopcs in thc HEUA cnrrgy rcgion
rii-LTiitlv clnslic priHluttion öl"/)0 mrsrms \vjis also stndicd for iiilcrninliatc Q* and for 5Gr\'! l Q2 < 311 GeV2. In t h»- ititcimrdialr Q! rrgion [l 13, 39) thc growth uf tlie I.TUSRscction with incrcasing !1\F is \vc;ik, consistcnt with (hat ohscrvcd in plinlopi-odnction. Dycnntrast, tlie criiss srction for clastic pn prodnction in dfcp inclaslic scallciing (Q2 S> 5GcV2)i'xhibits R strongcr \Y^V «Irpnnlnicc. Thc dctcrniinnlidii df ihr U'7I, di'|icndcncc of thc trossscction fruni a lit to thc loiv cncrgy lixcd targct mcasnrrmrnts |78, 39] and ihr rcccnt HERAniwisiircnicnfs [!()!), 52] is howcvcr diffitidt, sincc ihr t wo h>w rncrgy cx|H'vinu'nls cxhibit asignificaiit disagrccincnt. Tlicrcfurc tlir riwt- of thc rlastir pn ;is a fmictiim of \\\ in dccpinclastic scattcring was dctcnnincd froin thc ZEL'S data ahme [II] At largc Q7 (Q2 > 15GoV3) tlir 11'1P dcpciulcni'e nf die cross wction cxliiliits n rise which is faslcr than tlie oneprrdicted by the soft Pumcron niodcl. Again thc stnjtig risc of Ihc noss scrtion is consislcnlwith prrdictions by modcls bascd on pcrttirbalivc QC'D, in which thc risc is cxplaincd bytlie incrcasc of (lic ghion dcnsity in tlie protdn at sinall .r.
In contlnsion thc cross scrtion fdr clastic vrctor nicson prmlnrtion has a wcak dopendcncc.on H'7p, if thcrc is im liard scalr in thc proccss. Such a lichavior is sccn in c'lnstic /»", u and rj>photnpruduction. ßy ronlra.st, if a hnrd scalc is providcd. tlie cross scctidn for clastic vectornicsun prodnction cxhibits a slrong M'1P dcpendi'ticc. In pluHoprodnctidii of J/V incsonsthc niass of thc .//(/• incson prdvidcs thc hard scale and for vcctor nirsnii prodnction in dccpinclastic scattcring lln^ scalc is sei by Q2.
Appendix A
List of Hot Calorimeter Cells
In tlic 1994 datn tnking pcriod SOIHC calorimctcr channcls slmnvd addi t iona! noisr, visitjlc ästails in thc noispspcctra. For thc study ofdaslic p" pliotoprodiiclinii il is csscnlinl to idcntifyand rcniovc thcsc fflls from tlir analysis, brfnrc applying thc ml on l tu1 niusl nn'iRotic ccllapart from tlio tracks (srction 1.3.2). Thc rncrgj- fyr Ihrsc hol n-lls i t i t In- affrirtcd run rängeis sct lo zrro, JT it is liclnw a crrtain tlircsliold. Tliis Ilirrsliuld niininii/rs llic loss of pliysicsand is gjvrn by thc liiglicst rnrrgy dcpnsil in randnmlv tripgcrcd iMdits Tor räch hol ccll.Tlic list of all hot cclls with tlio corrcsponding cnrrgy throsliold and ttir nffcctccf run ranpris givcn in tablc A.I Tor thc diffcTcnt calorimctcr st-ctiims scp;n;itcly. In soiuc cascs tlic ccllwas c.xclndi'd fmni thi1 analysis cvon, if thc ccll was not isnlaicd, sinci* simc noisy cliannclsarc gruuprd.
131
\.\2 i(i\ I,isf t-f
ralonnipter
rell IDrun raiif;e
afTeclfHl
r i iPTRi MiTrstiolil(GeY)
exrliKtcd onlyif llie re!l is isolated
F H A C
8284G924
95IW-WU29890-9962
77-10C742G7442194
G2009858
9284 95.199284-100159284-97159284-101499509-1014995 7 5- WH»
0 40.5
yesyes
FEMC040.50.50.50.50.4
yesnonoDO
110yes
D I I A C294(14293902938829400200*1-42084C
293842819G29378293942938029.19623G5G215422325220308273482115820G74
2157427234
22552
292C61650028,1103128G307762S770
10584
95(19-99219509-99979509-90279509-99279000-99279044-9858
9509-99279509 100209509-992*9509-99209509-99279509-9927
9509-100159509-100009093-100509251-95939310-100389.110-100829509-96119968- 101499509- 100009509-977G
9915-I014Ü9G33-9G54
10007-101499G44-IOOGO9GC5-99209665-99979G93-101499843-9927
9900- H10299843-987-1
050.50.50.50 40.5
nono1>O
noyesyes
B EMC05O G05050505O ßO HO f i0 4040 41)404040 40.40.50.50.40.4000 4040 4
04
non ononon oHO
yesyesyesyesyesyesyesyesyesyesyesyesyesyesywyesyesyesyesyes
R I I A C
37210 9022-970! I 2 yes
Appendix B
List of Excluded Runs
Fur Ihr nnalysis prrsenlrd in th is thcsis only tho.sc runs , fnun thc 1991 d;il;i l ak ing prriod,n-ilh nomina l vrrtc.x and pnsitrnn braut wrri1 nsrd. fl inis fnim Ihr clcclron n i n n i n g pi-rii)din 1991 ivrir not nscd sincc tlic CTLT was not ralitinitnl Tor tlicsc runs, whicli rcsiihs ina lowcr rfficiciu'.v of tlio REMCn.i cnl . Pntis takpn af t r - r t l i r stiifti-d vn t i ' x nnis an1 alsorrjcctrcl, l>cc;iu«' in tlicso runs cslra noisc in ihr fonvjml t-alnrimcti-r .shoxvcd np (si'dioti4.1). Two sclcction criti-ria wen1 iniposcd on thc rcinaining rttus. A run sniitniarv rmist havoIM-PII crcatrd and Ihr timiinosity of tlu1 run luis lo hc t ' igRt 'r (.hau ylK) /*lr ' . To sclrc-t tlio.scnnis for \vhidi l'ic ZEUS drtrctor was ninning s la l i ly tlic mciin and R \ I S valm-s for cadirnn for l tu- followiug disUibutions jirc dctcrniincd: i-ncrgii-s in REMC, R I I A C , MC A L andFC'.AL und nmnlicr of hits in tlic CTD Tor each I rnck in thc nxi.il laycrs, slrrco l;i\crs ; inrl ?,l iy t i n i i n g layrrs. A r i r n was rrjcctcd. if thc d i s l r i l m t i n n in oiu1 of tdcsc var in l i lcs d i (fers ini ls nican valtic Ity untre tluin thrcc tinics thc RMS/\/W fntin (lic mcnn ovi-r »I I nn is (scrtinn\.4) T\vo indcpnidrnt TLT triggcr strcatiis \vcrc nscd in t l i i s analysis, so iwo lists nf bailruns \VITC ciralcd. All runs in n singk- HERA clcctron HM wcrc cxrli tdi1«! l rot n t l ic an;ilysis,if onc of tlic rnns in llic (itl is idt'ntificd äs a bad rnn fi>r um.' of Mir Ir iggrr sl icatns. A l lsnspicions f i l l s g tvr 'n liclow wcrc htiivcvt-r fmiml für I m l h triggcr strr;iins. A list i)f all runsrxclndrd fruni t l ic analysis, aftrr Uio Standard ZEUS rnn s i - lcct iot i , is givru in td l i lc B I.
Tablc A.l: Thc list of noisy caloriinctrr teils in 1994.
1.13
«l l-'.x'lii,!'-,! K.
iio n in sniniiiary:Imv Inminosity (< 500 yib"
snspidtius (ills
nin nnnibrr9271,9272,9299,9007,9637,99909252,9257,9270,9302,9305,9365,9388,9389,9390,9-110,9411,9463,9404,9509,9513,95 44,9500,9565,9560,9575,9602,9633,9650,9065,9700,9710,9794,9812,9872,9892,9909,9977,10028,10047,10074,10085,10091,10114,10118,101359250,9301,9304,9300,9310,9311,9312,9350,9351,9352,9362,9380,9381,9382,9385,9386,9387,9393,9394,9400,9107,9408,9412,9413,9534,9536,9536,9537,9543,9501,9507,9570,9571,9570,9577,9579,9581,9582,9084,9586,9587,9589,9590,9591,9592,9593,9022,9623,9624,9625,9626,9627,9628,9719,9720,9721,9722,9773,9804,9805,9800,9823
Tnlilt- B . l : List nf riins cxclmlcd fruni l l ip iinalysis aftrr applying thr Standard ZEUS runwirrt ion.
Appendix C
Tables of Data
{"'uOO».')
54 B
O
(,'b)10.90t 021
± 0.21
± 0.26
± 0.36
0 16±0.05
a,(l'b)
10.91± 0 2 1
10. W± 0.20
11.17± 0.21
11.34± 0.22
0.10
± 0.05
O-i
(üb)
11.23± 0.24
I0.7S±0.24U 20
±0.3211.17
± 0.43
-0.01±008
a>
(nM
10.07± 0.30
992±02010.49
± 0.24
10.6«±0.34
0.14
± 0.06
"4(l'b)
1 1 .57± 0 2 311.44t 02312.13t 0.28
12.52t 0.28
O.IB
t 0.06
"j
(l'b)
11.18± O.J2
11.02±012
11.65± 0.26
11.85± 0 3 60 14
± 0.06
0.
<l'b)
10.59t 0.21
10.47± 0.21
11.10± 0.25
11.48± 0.2fi
0.18
± 0.06
O,
("1>)12.03
± 0 1411.48
± o.n11 98
± 0 3 712.15
± 0.370.04
± 0.06
o.
(l'b)
i 0.20
10.13t 0.20
10.871 025II 24± 0.25
i 006
<»;,)(OV)
M. 8
"9
(l'b)
10.93± 0 3 1
± 0 2 1
±026
± 02B
± 0.06
C10
leb)
10.87± 0.2t
±0.21
± 0.26
± 0.26
±0.06
<T||
(fb)
10.91± 0.21
10.76± 0.21
1 1 ..19
±0.2611.63
±0.260.15
±0.06
Oll
(l'b)
1089
± 0.21
10. 7S±021
11.39±0.3611.71±0.26
0.17
± 0.06
fu
(l'b)
10.90± 0311076
± 02111.39
± 02fi11.67
± 0 2 60.16
± 0.06
fn
(l'b)
1090
t 0.21
10.76± 0.21
11.39t 0.26
11.67± 0.26
0 16± 0.06
<»I5
(•-h)
10.90± 0.21
1076
± O.J1
11.40± 0.26
11-64± 0.26
0.15
± 0.06
"l«
(cb|
10.90± 0.21
10. 7S± 0.21
11.38± 0 2 611.70± 0.36
0.16
± 0.0«
0ii(nb)
±03310.70t 02211.28
± 0 2 6II 55± 0.26
± 0.06
<»'„)(CfV)
0l«(«M
1094
± 0 2 1
±021
± 0 2 6
± 0 2 6
± 0.06
0 19
fl'b)
10.78±0.21
± 0.31
± 0 2 6
± 0.26
± 0.06
"10
leb)
1090
±0.2110.75
± 0.21
1 1 ..18
±03811.66
±0.260.16
± 0.06
0],
(nb)
10.89±0.2110.7J
±0.2111.38
± 0.26
11.63±0.26
0.16
±0.06
<>n
(l'b)
10.88± 03110.70
± 02111.23i 0.3.111.33± 0 2 50. 10
± 0.06
On
(l'b)
1090
± 0.31
10.81± 0 2 1
11.49t 02611.99± 0.32
020± 006
ff»
(üb)
10.99± 021lO.ao
± 0.21
11.38± 0.2J
11.51± 0.26
0.11
± 0.06
"n(üb)
10.80± 0.21
10.71± 0.21
11.39± 0.36
II 80± 0.26
0.30
± 0.06
0M
(l'b)
± 0.23
10.74± 0 2 3
11 33± 0.28
1 1.75
± 0 2 80 16
± 0.06
<»'W)(0-V)
54.8
Cjl
(l-b)
10.86± 0.21
± 0.21
± 0.2«
±0.3»014
±O.M
CM
(/•b)
10.91± 0.32
10.77± 0.22
11.42± 0.26
II 7l±027
0.16
± 0.06
OM(i'b)
1080
± 0 2 1
1065
±0.31M 28
± 0.26
11.67± 0.31
0 17±0.06
On
(l'b)
1066
± 0.21
10.52± 0.21
H 13± 0.2.>11 S2± 0.30
0.17
± 006
"M
(fb)
10.61± 0.31
10.46± 0.31
11 07± 0 2 5M 46
±0300.17
± 006
0SY
(Cb)
M 33± 0.22
11 19± 0.22
II 69± 0.2.111.76
± 0 260.09
± 0 06
Tiililr C.l: Tlic SÖding modcl cross section in \\\„ bins ohtfliiiod using corrrction inrilioti(n ) Thr rrtws scrtion for all systcrnalicchccks nffccting t l ip cross scction is givcn Tlic rrsiiltof (it willi a function of tlic type H'*(1 is givcn for cach chrck in thc boltoin l inc of thc fahle.
<»;,)«:*v)
54 R
64 9
74 9
S96
n
afpb)
10.88± 0.21
10-67± 0.19
M 15i 0.32
11.46i 0.22
0.13
± 0-05
o<
(Cb)
10.90± 0 3 1
10.47± O.IB
10.88± 0.20
M. .W± 0 1 9
0.10
± 0.05
ff]
(l'b)
II 38± 0 2 410-86
± 0.24
11.25± 0 2910-91
± 0.44
-0.06±0-08
"a
(M>)
10.07± 0.20
9.84
±0 .1710.28
± 0 2010. .W
± 0210.11
± 0.05
r>4
ff*')
1 1 .55± 0.22
11.35± 0.20
II. 87±0.2312.27
± O M0.14
±0.05
"s
(«><)
11.17± 0.22
10.91± 0 1911 4l
± 0.22
11.67i 0130.11
± 0.05
PS
(l'b)
10.57± 0.2!
1039
± 0.18
10.86± 0.21
11.24± 0.33
0.15
±005
O,
</'b)
12.02± 0.33
11.40± 0.30
11.75t 0 2.111.94
± 0.23
0.01
±005
c,
(*'>>)
9.99
± 0 1 9
10-M
±0.171062
± 0.21
11.03± 0 220,23
±0.05
O»',,)(««V)
09
(Cb)
10.92± 0.21
1072
± 0.19
1 1 .2.1
± 0.22
11 50± 0-23
0.14
± 0 0 5
0,0
(l'b)
1085
± 0.21
1062
± 0.19
11.08± 0.22
l t . 38±0.330 12
± 0.05
Oll
(l'b)
10.90± 0.21
1067
± 0.19
11.14± 0 2 2II 43
±0220.12
± 0-05
".I
</'b)
1087
± 0 2 1
10. fiS± 0 19II 16
± 0.22
11.50±023
O. t3
± O.O.i
0\3
(/•'')
1088
± 0.11
10.67± 0.19
11.15±02211.46
±0220.13
± 0-05
ff,.
leb}
10.89± 0.21
(0.67±0.1911. IS
± 0 2 2II 46
± 0.32
0.13
± 0 0 5
<T|S
(i-b)
10.89± 0.31
10.67± 0.19
11.15± 0 3311.46
± 0.22
0.13
± 0-05
c.«(l'b)
10.88± 0.21
1067
± 0.19
11.15± 0 2 311.46
± 0220.13
± 005
»II
(l'b)
10.86±02210.61
± 0-19
11 04± 0.22
11. M± 0-23
0.11
± 0.06
O''-,,)(c:*v)
C|«
(M
1093± 0.211072
± 0.19
11 20± 0.22
II 53± 0 2 3
0.13
± 0.05
"nleb)
1073
± 0.2t
10.50± 0 1 8
10. 9t± 0 2 1
II 2l± 0.22
0 . 1 1
±005
a, u
(/.h)
10.89±0.2110.67
± 0.19
11 15± 0.22
11 46±0220 12
± 0.05
TU
O'b)
10.88± 0 2 1
10.66± 0 1911.14
± 0 2 211. 4 i
±0220.12
± 0.05
OH(ph)
1086
± 0.21
10«± 0.18
1092
± 0.21
11.17± 0 2 2008
± 005
"11
(;-b)
10«)
± 0 2 1
10.79± 02111 37
± 0 2 2ll.7.i
± 0.24
0 17± 0.06
"H(«•!>)
10.98± 0.21
10.66±0.191108t 0.2211. .15
± 0.22
0.09
± 0.05
<7jj
{!•'>)
1 0.78
± 0.3l
I061
±0.1911.19
± 0 2 211.54
± 0.23
0 16± O.ftj
(7)0
(/'M
11.10± 0 2 310.70
± 0.2fl1 1 . 1 7
± 0.2.1H. -T«
±0.24011
± 0.06
(»'.P)(C*V)
C]l
(l'b)
10.83± 031I0fi3
± 0.19
11.12± 0.32
11 39± 0.22
0 12± 0.05
Cji
(l'b)
1084
± 02110.64i 0.19
11.17± 0 2 211.48
± 0 2.10.14
± 0.05
"JJ
llibf
1076
± 0 2 1
1060
± 02111.26
± 0.25
II 48± 0 2 70 15
± 006
"31
(l'b)
1051± 0211046
t 020N 11
± 0 3 4II .12
± 0 2 70 15
± 0.06
"3,
(I.M
JU.86i 021m. 70i 02t
1 1 .36± 0251 1 .59
± 0.27
0 15± 006
CM(Jtl.)
1092
± 0 2 1
10 74±021
11.17± 0.23
11.12± 0.23
009± 0.0.5
fj7
(üb)
10.87± 02t10.65
±019
1 1 . 1 7± 0 2 211.61
± 0.23
0 16± 0.05
(Tcjy
(J'b)
II 44± 0.22
11.2.1±02011.74
± 0 2.112.06± 0 240 13
± 0.05
Talilc C 2: I.ikc labte C.l bul thr Södmt) rnodd crots srrtwn incurrcction nirttiud (b).
hiiis obiaincd using
l -'S 5"
n10
i J5"
3
t~2. s
l i!f* ~=• oo
o . o
^ => •
=•
—
w' ij
*»
*-
^ *
_ ^ «
*+•
_
O
- O
-
O
— H
- _
H-
_. M
- —
1(1
<»'>,)(' '"V,
54 »
n
ll'M11 2.5
± O2fi
± 0 3 6
± 0.31
± 0 3 50.16
± 006
"i(1.1.1
13.22i 0 36
± 0.24
± 0.79
± 0 3 1
0.12
± 006
«j
((•!')
13 71± 0 2 9
± 0.29
± 0.19
± 0 6 4•O.DI
± 0.09
C,
(,.10
1225
± 0 2 4
± 0 2 413.78
±0.79
± 0 3 1
0 14
±006
a.0-M
1406
± 0.38
1392
± 02714.76
± n .131524
± 0 3 80.18
± 006
«>
(ML)
13.60± 0 2 7
1 3 4 7
± 0 3 614.20
± 0 3 214.48
± 0 3 4
0 IJ± 0.06
"n
'"''>12.86
± 0.23
13.74± 0.23
(150
± 0 1 1
13.97t 0.35
0.18
± 0.06
"70-10
1 4 6 2
± 0291398
± 0 2 814.59
± 0 3 314.83
± 0 37004
± 0.06
ff
(l'l'l
±0.2417.33
± 0 7413.7.1
± 0.30
I3.fi9±037
0.26
± 0.06
{»'•.,)(<->V|
(T,
(*'h)
13.30± 0 2 6
±026
±032
±035
± 006
CID
(lil't
1 3.2 1± 0 2 6
± 0.2fi13.77± 0.31
t 0.34
± 0.06
"n(l'l.)
13 '26± 0 2 6
± 0 2 611 HG
± 0 3 1
14 17
± 0 3 4
± 006
Cu
lüt.)
11.24± 0 3 6
± 0 2 613 »K± 0 3l1 4 3 1
±0360.17
± 006
(Tu
((.'>)
13.25± 0 3 613.10
± 0.2*
11.87± 03114.74
± 0-35
0.16
± 0.06
"l.
ll'b)
1 3 2 5
t 02fi1l 10
± 0.26
1387
± 0 3 1
1 4 2 4
± 0 3 3o.ie
± 0-06
ffll(l'b)1336
± 0 2 611 II
± 0261 3.88
± 0.31
14.32± 0.33
0.16
t 00«
»!•
l/'l.)
13.25± 0 2 613.09
± 0 2 613.K6± 0.31
1425
± 0.34
0.17
± 0.06
0,1
(l<b)
13.22±0.261302
± 0.26
13 74± 0 3114.08
± 0 3 60 14
± 0.06
("'i,)<i>V|
54 8
0,f
{(«!')
1129
i 0.26
± 0.26
± 0.33
± 0.35
± 006
"...
(••!')
U. 10± 0 2 612.94
± 0.26
13.70± 0.31
± 0.35
± 0.06
(7,0
(('!.)
13.25± 0 7 61309
± 0.26
1.1 %± 0 3 1
14 21± 0.34
0 16± 0.06
"n
(..l.l
13.24± 0 7 6130»
± 0 2 61.185
± 0 3 1
14 20± 0.350 16
± 006
o„
((.'•)1.1 12
± 0 2 61294
± 0.26
136«
± 0.11
118»
± 0.31
0.13±006
Cu
(*.!•)
1 3 3 7
± 0 2 613.75
± 0.26
14.06t 0.32
|4 56± O.M0 19
± 006
fj.
(»'!')
13.13t 0.26
1303
± 026(386
± 03114.17± 0.380.20t 006
",s
(('!>)
± 02611.1.5± 0.26
1385
± 0 3 011.98
± 0.31
± 006
a M
<(•!')
± 02«1304
± 0.28
13 64± 0.29
1391
±0.33
± 0.08
O»-'»)(t:* v)
54.«
64 9
749
89.6
a
"i.(»'!>)
1.122± 0 2 613.10
± 0.26
1 3 7,1± 03114 IG± 0 3 5
0 1.5± 0 0 6
a„().'>)13.32
± 0.2fi13 17
± 0.2G
1398
± 0.32
14.37±0380 17
± 0.06
a„(i'ii)
13.19± 0.2G
13.03±02613.80
± 0 3 1
14.22± 0 3 801T
± 0.06
0»
(Ml*)
1328
± 0 2 613 12
± 0 2 613.90
± 0 3 1
14 19±031
0 15± 0.06
Cjj
(Ml-)
1321± 0 261306
± 0 2 613.83
± 0 311 4 2 4
± D.3»
0.17
± 0.06
T;ilili' C ö: Likc t i i l i l r C.l liut t l ip phrnommolofiical Söding mottet cross srctian in Il'1p l» ins»sing corrciiiun nu'tliod (a).
141
("\,1
548
649
7 4 9
896
(l
ff
1 2 15± 0 2 413.17
± 0.34
12.85± 02513.12
± 0.31
0.14
± 0.06
(MM
II 9»± 0.21
11.58± 0 2 212.27
± 0.24
12.59± 0 25013
± 0.05
"7
(/•D
H 45
± 0 2 91386
t 0791329
± 0.37
1281
± O.J2
-0.0?± 0.08
öt
11 42± 0.22
11 23± 0.72
11 83± 0 2312.02
± 0 2 80.12
± 006
O,
O.M
n 11± 0.2.5129*
i 02.5
13 G»± 0.27
14.04±0330.16
± 0.06
"i
12 BH± 0 3 51247
± 0 7 411 14
±07613.37
± 0 3 1
0 13± 006
0.1.)
11 99± 02.1
II »4± 02113. -.3
± 03512 8C.
± 0 3 00.16
± 0.06
n,
1362
± 0 2 71799
± 0 2513.52± 0 2 71365
± 0.32
002± OOfi
(M'-,
11.3t± 0.32
11 46± 0.22
12.33± 0 241265
±0.300.24
±0.06
S.54 a
649
74 9
896
a
a a
12.39± 0 3 412.24
± 0 7 41294
± 0.25
13.23± 0.31
0 15i 0 06
"10
(Ml>)
12.31± 0.24
12.11± 0 2 412 76
± 0.25
13.02± 0310 13
±006
"n
12.3?± 0 2 412 1»
± 0.34
128.1± 0.2-51109
± 0310 13
± 006
0,1
12.11± 0 2412.16
± 0-24
± 0.23
13 16± 0-31
0 15± 006
a„
12.15±02412.17
± 0.24
1285
± 0.25
13 12± 0.31
0-14
± 0.06
(l'M
± 0 2 417 17
± 0.24
1 2 8 5
± O7.i
1.1.12± 0 1 1
0.14
± 0.06
"n
(MM
12 T.± 0 2 4[2.17t 0.74
17. S 5± 02513 12
± 0 3 1
0 14± 0.06
*,„
1 2 3 5
± 0 3 412 17
± 0 241284
± 0 2513 12
± 0310 N
± 0.06
('hl
12.32± 0.25
12.10± 0 2 412.77
± 02.5
12.97± 0310 12
± 006
<"',„>(t:-v)
548
64 9
749
»96
a
»l«
12.39± 0.24
12.22± 0.24
12.89± 0.23
13.20± 0.31
0.15
± 0 06
n,,.
12.20± 0 2 412.00± 0.21
12.6»± 0.35
1285
± 0.30
0 13± 0.06
(/.l.)
± 0 2 4
± 0 2412.84i 0.25
1.1 12± 0.31
0 14± 006
S.1.12.34t 02412 15
± 0 2 41282
± 0.25
M 10± 0.31
0.14
± 0 0 6
"n{/•'•l
1323
± 0 2 4U 02± 02317-58
± 0 2 51288
±010
0,12
±006
«JJ
12 4P,± 0 2 412 11
± 0 241 3 10i 02911 16
± 0.31
0.16
t 0.06
"n
0.1.)
1 2 2-1f. 03112 12
± 0.24
(291
± 02»13 20
± 0 3 1
0 18± 0 0 6
ll'l'l
1 2 4 5
± 02412 17
± 0.71
12*9
t 0 2.51301
± 02*0.11
± 0.06
"TU
12. .50± 02«12.04± 0.72
12.56± 0.2B
1100
t 0.27
O.M± 006
S548
649
74.9
896
a
"Ji
(l'l.)
1 2..15± 0.24
12.17± 0 211288
± 0.25
13 14± 0.31
0 15± OOG
"n
1728
± 02412. Ij
± 0 2 41292
i 02613 18
± 0.31
0 17± 0 0 6
("",
1228
i 0 2412-10
± 0 2 41 2.8-1
± 0.7«
13, «i± 0.31
0.15
± 0.06
(M'' (üb (iil)) (,,!,)
I2..3S 1231 1255 12.09t 0.21 ± 0.24 ± 0 2 4 t 0.2412.20 12 11 17.15 1203
4 074 ± 0.24 ± 0.24 ± 07312.8.1 12.87 11.00 12.72
± 0 3 5 A 0.2» * 0.27 ± 02513.15 1309 I3.0i 13 6
± 0.3) ± 011 ± 031 i 0310.14 0.14 0 0 1) 19
± Q.W: ± 0.06 t 0.06 ±006
C.ß: Likc tJiMt- C.l bnt ihc phrnornrnological.' iising currcction nKiliud (h).
modfl cross srctwn in II' hins
(im(G
. V)
0.006
0.018
0.034
0.036
0.084
Q.l IS
0.1
SÄ
0.224
u.345
Ifl/.-M
({J«
^""l
0.789±
0.0
42
0.7
77
±0.0
27
0.7
29
±0.0
19
0.7
2!
±0.0
24
O.M
3±0.0
28
0.638±
0.0
32
O.flH
±0.0
31
0.509±0.0
29
0.375±
0.0
28
6\B
/A\,
(G«
V-'")
+0.0
25
-0.0
04
-cO.038
-0.004+0.0
27
-0.0
04
+0.0
38
-0,004«-0.03O-0.004+0.0
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•0.004+0.0
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-0.0
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-0.0
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n
i.96
± 0
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± 0
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18
4.91±
0.1
74.73
± 0
.20
4.05± 0
.10
3.11±
0.21
6n,
+0.1
5-0.00-0
16-0.00+0.16
0.00+0.17-0.00+0.18•0.00-0
. 19-O
.UO
-0.2
0-0.00+
0.2
2-000+0.2
6-0.00
<K
i
+0.0
0-0.00-0
00
-0.00+0.0
0-0.00-0
.00
0.00+0.0
0-0.00+0.0
0-0.00-0
.00
-0.00+0.0
0-0.00+0.0
0-0.00
än
,„
+ 0.02
•0.02+0.0
2.0.02-0
.02
-0.01+0.0
2-0.01+0.01-0.01+
0.01•0.01+0.01•0.01+0.01-0.01+
0.0
1•0.01
<f'li.+
0.0
10.0
1
-ooi
•0.01+0.0
1-0.01+
0.01-0.01+
0.01•0.01+0.01-0.01+0.0
2-0.02+0.0
2-0.02+
0.0
2-0.02
6n,
+0.0
0-0.00+0.0
0-0.00+0.0
0-0.01+0.0
0-0.01+0.0
0-0.01+0.0
0•0.01+0.0
0•0.02+0.0
0-0.02
+0.01-0.03
6n
„
-0.0
0-0.00+0.0
0-0.00+0.0
0-0.00+0.0
0-0.00+0.0
0-0.00+0.0
0-0.00+0.0
0-0.00+0.0
0•0.00+0.0
0•0.00
<S
n.,i
+O.O
B-0.06-0
.06
-0.06+0.0
6-0.06+0.0
«-0.07+
0.0
7-0.07+0.0
7-0.07+0.0
7-0.07+0.0
7-0.08+0.0
80.08
dfij.
-0.0
0-0.01+0.0
0-0.03+0.0
0-0.03-0
.00
-0.0«+0.0
0-o.os+0.0
0-0.07+0.0
0-0.09+0.0
0-0.13+0.0
0-0.20
an.
-00
2-0.00+0.0
3-0.00+0.0
3-0.00+0.0
3-0.00+0.0
4-0.00+
0.0
4-0.00+0.0
5-0.00+0.0
6-0.00+0.0
8-0.00
Ort..
1-0.00-0 II
-O.U
Q
-0.il
+0.0
0-O
.ll+0.0
0-O
.ll+
00
0-Q
.IO+0.0
0-O
.IO+0.0
0-O
.IO+0.0
0-0.09+
00
0-0.07
Tablc C
.7: The ratio |ß
/.4| and thc param
eter n, mcasuring thc am
ount of skowing, (Vom
fits to thc invariant niassdistnbution according to cqualions (9.7)
and (9.10) in |(| bins. T
h« systcmatic errors obtaincd for
the crror classosaffccting the result are also given.
S
2
S
~ P
S 9
bjl
Sa
P9
9
H-
_
H-
_
H-
_
; 8
M „. «
«
p .
O ;
or- S
yo —
o [T o °1
H-
_
H-
— H
- _
_
H-
_
H-
_
- o
« S
^ £
'S54.8
649
RIO
-.'„K*V->,
(ir,p}
54. R
619
84.0
nt(O.V-|
(ir.,,)ir .«v )
348
6 4 9
840
,.'r(c«v->,
SS54-8
6 4 9
R4.0
«• r(«fV-')
S54.8
64.9
840
o'p.lC.V-»)
6(OV-'I
1331
± 0211266
±02012. «4
± 0.14
028± 0.14
(C/J-')
1229
± 0 2 1
± 0 1912*5
± 0.14
0.39
± 0.14
fr,.
l<.fV )
1279
1264
± 0.30
13 »2± 0 14
0.28
± 0.14
(OV-'J
1230
± 02112.63± 0 2 01283
±0.1402»
± 0 1 4
fr«
1234
± 0 3 41366
± 0 2 01282
± 0.16
02S± 0 16
fr,
11.09± 0.22
12.32i 0 1812.54
±0.13025
± 0 1 4
fr.
1230
i 0221264
±03012.81
± 0.14
0.37
± 0.14
fr„
(l.*\
12 .W± 0 2 1
1266
± 0.30
1283
± 0 1 4
038± 0.14
,<>;•'',13 33
± 0211269
± 0.30
1288
± 0 14029
± 0.14
c«-,1241
± 0 2 412 76
± 0.21
1284
± 0 140.21
± 0.15
b,
12.33± 0.24
12.37±02213.41
± 0.21
0.02
± 0.18
fr,
1230
t 0.21
1264
t 0201281
i 0.14
037i 014
b,.
(f>\
12.32±0.21136«
± 0.20
1283
t 0 14027
t 0.14
bn
12.31± 0.21
12.65t 0.20
11.81t 0.14
026± 0.14
(0V-')
1226
± 0.20
12.65± 0.19
12.97± 0 14039
± 0 16
6,
1262
± 0.23
1289
± 0.20
13.07±0.13
0.24
± 0.15
«£->}
12.32± 0-21
12.69± 0.20
1286
± 0.14
0.28
± 0.14
fr,;
(G*V )
13.36± 0.22
12.72±02012.90
± 0-IS
0.19
±0-13
[0V-')
1263
±0-2112.98
± 0-20
13.17±0,14
0.29
±0,H
fr»
1233
± 0.22
1257
± 0.20
1273
± 0.14
026± 0.14
fr«
12. M± 0.21
12.47t 0.19
± 0.14
0.28± 0.14
(ÜfV1)
12.30± 0.21
12.60± 0.20
1282
±0.140.27
±O.H
fr,.
(GeV )
13.31± 0.21
12.67± 0 2012.83± 0.14
0.27
± 0.14
(cU-M12.00
± 0 2 21235
± 02012.51
± 0.15
0.26
± 0 14
fr»
12.43± 0.21
12.81± 0201299
± 0 140.38
i 014
61
± 0 2312.47
± 03012.65
± 0.14
024± 0 1 3
(<i'-,
± 021T2.671 02012.83
± 0.14
± 0 1 4
fr,.
( '1231
± 0.12
I2«6± 0.21
1283
± 0 1 5
0.28
± 0 15
fr«
± 0.70
1291
± 0.6«
1234
± 0 5 3001
J 0 49
6«
12.14t 0 3 11269
±0201285
± 0 14027
± 0 14
6.
± 0.21
1267
± 0 1912.83
± 0.14
± 0.14
bn(»V-»)
± 0.2l1768
± 0.20
13.85± 0.14
i 0.14
fr»(C* )
1331± 0311766
±0.201283
± 0.14
± 0 1 4
b»
(t:* v-')
± 0 7 1
12.90± 0671354
± 0 54001
± 0.50
T;iMe C,9: Liko lablc1 C.8 luit Tor Mir parnntetprization cross srction
(»'„><ov)
54.1
649
84.0
nr |G«>V->)
("S,)(t:«vj
M. S
64.9
«4.0
"'T, <OV-')
O'',,)(t;«v)
54 8
649
1140
«^ItifV-')
('»•,r)tov)
54 8
fi4.9
84.0
»i, [IfcV-»)
<»\P><OV|
W. 8
649
8-10
..'p (0V-')
fe
(CeV-'j
1090± 0.21
II 14± 0 2011.34i 0.15
0.24
± 0.14
67
(t:»v-M10.01
± 0 3 1
t l .16f 0.19
11 33±0.14
0 2 4± 0.14
fr M
(O.V-»)
1088
± 0.31
II 12± 0.30
M 32± 0 1 5
024± 0.14
b>,(Ov-'j
10.89±011
11.13±02011,33
±0-15O.S4
± 0 1 4
bjo
(t>V-'(
10.92± 0 2 411.10
± 0-20
M 17± 0 1 6
0 19± 0.15
6.(<;ev-')
10.80± 0.72
II 04± 0 1111.23
±0.13021
1 0.14
&8
(0V1)
10 H»±0.2211.11±020
T 1.30
± 0.1S
0.23
± 0 14
fr„
(0V-1)
10. »9± 0.21
II 13t 02011.34
± 0.15
1)25
± 0.14
fc„
tc:*v-')1087
± 0.21
11.11± DM1II 32
±0.14025
± 0.14
*j.(t;»v-*i
11 0.1± 0 2 411 27
± 0.21
H 33± 0.15
0 M±014
b,
(ov-')
IOS2•h 02410.91
± 0.22
10.92f 021
0.05
± 0.18
fr,.
(0V-')
10. 8«± 0.21
11.11± 0.20
H 3l±0.150.2.1
± 0.14
fr,.(ov-'j
10.90± 021II. M
±03011.13
± 0 1 4
0.21
± 0 14
b>,(CeV-'l
1092
± 0 2 1
11.16± 0.20
1 1 .35± 0.15
0.2.1±0 .14
frj,
[Crt-'(
10.90± 0 2 0M 17t 0.19
11.49± 0 1 4
03.1
± 0 1 4
frj
(OV-'j
II 21± 0 2 1
1 1 ..16
± 0.20
1 1 .5«±0.1>020
± 0.15
frm
(UfV-' j
1091
i 02111. IC
± 0.20
II .16± 0 1 4
025± O.M
fe„
(»>v-'j
1094
± 0.22
11.20± O.?0
II 42±0.15
0-2fi± 0 15
b„(OV-i)
11.21± 0 2 1
11.46± 0.19
11 67± 0 14
02.5
± 0.14
bu(C-V)
1092
± 0.22
11.17± 0.20
II 36±0.1.5
0.24
± 0 1 4
6.
(0V-')
1069
± 0 2 1
1094
± 0.19
11.14±0 .14
02.5
±0.14
6,.(CfV)
II) f>9t n iiU 13±0201 1 ,1.1f 0.15
O J 4±0.14
fr,'
|G*V-')
Hmt 021M 1.11 020II 1-1
± 0 M0 2 4
± 0 1 4
b„
io\)10 591 (122
1082
1 020II 01i 0 Ü021
± 0 15
*H(ov-')
10.90i 021II. Mt 120II 14i 0.14
034± 0 15
fr,
(0V-')
10.79± 0 2 310«
±03011 l.>
± 0.15
0.31
± 0.15
b„
«>v-'|
10. W± 0 2 1
1 1 . 1 4± 020II 1>
± 0 1 5
02i± 0 1 4
6,,(c;*v-'>
10.92-f 022II. IH
± 02011 37
± 0 1 5
02i± 0 1 5
fr»
(ov-'l
II 02±019
M 16± 0 6 4II 4l
± O..JO0 19
± 0 4 7
fr«
(UfV ')
10. <H)± 021H i:,
± 0 2 0II 15
± O.IS
0 2 4± 0.15
fr.
(OV-'J
1093
± 0 2 1
11.14± 0.19
11,33± 0 .14023
±0.14
bn(i>v->)
10.91± 0.31
11 15±02011.35
± 0.15
0 2 4± 0.14
bn
{i:*v-J)
10.90± 0.21
II M± n. 20II .13
± 0.15
024± 0.14
b„
(f>V-'|
11.01t 0.70
M 17± 0.68
11 24±053
0.12
i 0 49
Tal)lc C.lll. Likc Uihlc C.8 Init for tlii- phcnomr-notofiiral Säding inodei croan scclion.
(M.-.-)(<J«vJ)
0.617
0.688
0.721
0.746
0.769
0.797
0.838
0.951
f>(G.V-'J
I3.J4± 0 1911.80
± 0,26n.78
± 0.3011.90
± 0.3111 -27
± 0-2810.04
± 0.2710.11t 0.21883
±0.14
dfri(C.V-'(
+0.00.0.16+0.00-0.24+0.00-0.28+0.00-0.31+0.00-0.33+0.00-0.37+0.00-0.11+0.00-0.54
Öfci(C«V-J)
+0.2S-0.22+0.25-0.22+0.25-0.22+0.25-0.22+0.2S•0.22+0.25-0.22+0.25-0.22+0.24•0.23
<ffrm(C«V-J)
+0.04-0.03+0.04-0.03+0.04
-0.03+0.04-0.03+0.04-0.03+0.04-0.03+0.04•0.03*0.04-0.03
Sb-,.(C.V-'l
+0.05-0.06+0.06-0.05+0.06-0.04+0.0«-0.04+0.06-0.04+0.06-0.03+0.06•003+0.07-0.01
Jbv
(GW)
+0.11-0.02
+0.09-0.02+0.08-0.02+0.08-0.02+0.07-0.02+0.0«-0.01+O.OS-0.01+0.02-0,01
Sb„(CeV)
+0.00-0.00+0.00-0.00+0.00-0.00+0.00-0.00+0.00-0.00+000-0.00+0.00• 0.00+0.00-0.00
dbv„|t;.v-')
-026-0.26+0.27-0.28+0.27-0.27+0.27-0.27+0.27-0.27+0.28-0.27+0.18-0.28+0.29-0.29
6b.,H(C.V>)
+0.07-0.12+0.06-0.19+0.05•0.22+0.05•0.24•••005-0.26+0.04-0.29+0.03-033+0.01-0.43
ft>i.(C«V-J)
+0.00-0.06+0.00-0.06+0.00•0.0«+O.OO-0.06+0.00-0.08+0.00-0.07+0.00-0.07+0.00-0.07
«56,(<J.v-J)
+0.02-0.00+0.03-0.00+0.03•0.00+0.03-0.00••-0.03-0.00+0.04•0.00+0.04-0.00+0.05-0.00
Tablc C.ll: The slopc parameter 6„ obtained from fits according to equation (9.14) in A/»*»- bins.systematic crrors obtained for the crror classcs affectmg the result arc also givcn.
ThcE
(1*1) (OV])
0.008
0.018
0.034
0.056
0.084
0.1 13
0.158
0.224
'
-04r(»
0.033±0.03«-0.027±0.033-0.021±0.0300.040
±0.028-0.016±0.0250.011
±0.0260.029
±0.021-0.018±0.015O.Q4S
±0.0 1 7
fr;+0.00)-0.021+0.003•0.020+0.004-0.020+0.007-0.019+0.010-0.018+0.013-0.016+0.0 18-0.015+0.025•0.012+0.039-0.007
fr«
+0.000-0.000+0.000-0.000+0.000-0.001+0.000-0.001+0.000-0.001+0.000-0.001+0.001-0.001+0.001•0.001+0.001-0.002
fri..+0.003•0.005+0.003-0.004+0.003-0.004+0.003-0.004+0.003-0.004+0.003-0.004+0.002-0.004+0.002-0.003+0.002-0.002
<fr„
+0.003-0.005+0.003-0.004+0.003•0.004+0.003-0.004+0.003• 0.004-0.003-0.004+0.002-0.003+0.002-0.003+0.001-0.001
t».
+0.000•O.OOQ
+0.000-0.000-0.001•0.000+0.001-0.000+0.001•0.000+0.001-0.000+0.001-0.000+0.001-0.000+0.002-0.000
fr, i
+0.000-O.OOT+0.000-0.000+0.000-0.000+0.000-0.000+0.000-0.000+0.000-0.000+0.000-0.000+0.000-0.000+0.000-0.000
fr-..+0.003-0.00»+0.003-0.009+0.004• 0.008+0.004•0.008+0.005•0.007+0.00«-0.007+0.008-0.006+0.010-0.005+0.014-0.002
fr.
+0.007-0.005+O.OO6-0.004+0.006-0.004+0.006-0.004+0.005-0.004+0.005-0.003+0.004-0.003+0.003-0.002+0.001-0.001
(|t|> (GeV)
0.006
0.018
0.034
0.056
0.084
0.115
0.153
0.224
0 145
-.0*roo
0.072±0.0380,006
±0.0330.002
±0.0340.012
±0.028-0.016±0.0250.027
±0-0320.010
±0.0280.000
±0.0170.060±0.021
fri
+0.000-0.023+0.000-0.022+0.000-0.021+0.000•0.020+0.000-0.019+0.000•0.017+0.000-0.014-0000-0.011+O.OOO-0.004
frii+0.000-0.000+0.000-0.000+0.000-0.000+0.000-0.000+0.000-0.000+0.000-0.000+0.000•0.000+0.000•0.000+0-000-0.000
frii.+0.003-0.005+0.003-0.005+0.003-0.004+0.003-0.004+0.003-0.004+0.002•0.004+0.002-0.003-0.002-0.003+0.001-0.002
fri.
+0.002•0.004+0.002-0.003+0.002-0.003+0.002-0.003+0.002-0.003+0.002-0.003+0.002-0.002+0001-0.003-0.001-0.001
(fr.
+0.002-0.001+0.002-0.001-0.002•0.001+0.002-0.001+0.002-0.001+0.002•0.001+0.002-0.001--•0.002-0.001+0.002-0001
fr..
+0.000-0.000+0.000-0.000+0.000-0.000+0.000•0.000+0.000-0.000+O.OOO-0.000+0.000•0.000-0.000•0.000t- 0.000-0.000
fri.+0.001•0.006+0.001-0.006+0.001-0.006+0.002-0.006+0.002-0.005+0.002-o.oos+0.003•0.005+0.004•O.OO4+0.006-0.002
fr.
+0.009-0.030+0.010-0.029+0.010-0.028+0.0 1 1-0.028+0.012-0.024+0.013-0.022+0.01S-0.019+0.017-0.014+0.021•0.005
Table C.12: The spin density matrix clcmcnt rf^ äs obtained from fits accordingto equation (3.72) (iipper table} and cquation (9.17) (lowcr table) in \t\. Thcsvstematic errors obtained for the error classcs affecting thc result are also givcn.
(1*1) (GeV'J
0-OOA
0.0 18
0.034
O-O36
0.084
0.1 15
0. ISS
0.224
0. 345
»-04rio
0.060±0-0150.004
±0-015-0,007±0.014-0019±0-010
O.DO)±0.0160.013
±0-0160.014±0.0130.000
±0.0130.006±0.011
&r.
+0-004-0.018+0.004-0.01 B+0 .004
-0-018+0.004-0-017+0.003-0.017+0.003-0.017+0.003-0.016+0-002-0.015+0.001-0.014
frii
+0.000-0.000+0.000-0.000+0.001•0-000+0.001-O-OOO
+0.001-0.000+0-001-0.000+0.003-0.000+0.001-0-000+0.003-0.000
Srw
+0.001-0-001+0.001-0.001+0.001•0.001+0.001-0-001+0.001•0.001+0.001-0001+0.001-0.001+0.001-0.001+0.001-0.001
Sr-„
+0.001-0.001+0.001-0.001+0.001-0.001+0.001-0.001+0.001-0.00?+0.001-0.003+0.003•0.00!+0.001•0.003+0.003•0-001
<ir.
-r 0,001-0.002+0.001-0.003+0.001-0.002+0.001-0.001+0.001-0.001+0.001-0001+0.001-0.001+0.001-0.001+0.001-0.001
Sr„
+0.000.0,000+0.000-0.000+0.000-0.000+0.000-0.000+0.000-0.000+0.000-0.000+0.000-0.000+0.000-0.000+0.000-0.000
6rim
+0.000-0.002+0.001-0.003+0.001-0.001+0.001-0.001+0.001•0.001+0.002-0.001+0.003-0.001+0.004.0.001+0.007•0.001
<5r.
+0.001-0.018+0.002-0.017+0.004-0.016+0.006-0.015+0.010•0.014+0.013•0.013+0.018-0.011+0.025• 0.008+0.038-0.003
Table C.13: Thc spin densily matrix cicmcnt Sr^ äs obtained from fits accordingto cquation (3.72) in f(| bins. The systematic errors obtained for the crror classesaffecting the result are also given.
(|t|> (CeV)
0.006
0.018
0.034
0.056
0.084
0.1 IS
0.158
0.224
0.345
r°* r1-[
-0.036±0.0260.033
±0.0240.039
±0.023-0.030±0.022-0.022±0.031-0.039±0.0*20.005
±0.021-0.038±0.018-0.011±0.018
0>i
+O.QOO-0.005+0.000•0.006+0.000-0007+0.000-0.009+0.000-0.010+0.000-0.012+0.000-0.015+0.000-0.019+0.000-0.027
är-,i
+0.000-0,000+0.000-0.000+0.000-0.000+0.000-0.000+0.000•0.000+0.000-0.000+0.000-0.000+0.000•0.000+0.000-0.000
6r».
+0.001-0.001+0,001-0.001+0.001-0.001+0.001-0.001+0.002-0.001+0.002-0.001+0.003•0.001+0.002-0.001+0.003-O.OOJ
6r„
+0-004-0.002+0.004-0.003+0.005-0.002+0.005-0.002+0,006-0.002+0,006-0.002+0.007-0.003+0.008-0.003+0.010-0.004
tr.
+0.001-0000+0.001-0,000+0.001•0,000+0.002-0.000+0.002-0.001+0.003-0.001+0-003-0.001+0.004-0.001+0.006-0.002
fr..+0.000•0.000
+0.000-0.000+0.000-0.000+0.000-0.000+0.000-0.000+0.000-0.000+0.000-0000+0.000-0,000+0.000-0.000
fr«+0.001•0.000+0.001-0.001+0.001-0.001+0.001-0.001+0.001-0.002+0.001-0.002+0-001-0.003+0-001•0-004+0.000-0.007
ör.
+0.000-0.003+0.001-0003+0.002-0.003+0.002-0.003+0.004-0.003+0.005•0.002+0.007-0-002
+O.OO9-0.002+0.014•0-001
(Kl) (CeV*)
0.006
0.018
0.034
0.056
0.084
0.1 IS
0. 158
0.224
0.34S
roir1-i
-0.047±0.022•0.052iO.0240.054
±0.021-0.026±O.QJ3-0.014±0.0230.015=0.0140.036
SO.0220.039±0.0210-023
±0.019
ör,
T-0.003•0.009+0.007-0.010-0.012-O.QII-O.OM-0.013+0.030-0.016+0.04 1-0.019+O.OS6-Q.U24+0.079-0.030+0.1 W•0.043
<Sr„
+0.000-0.000+0.000-0.000+0.000•0001+0.000-0.001+0.000-0.001+0.000-0.001+0.000-0.001+0.000-0.002+0.000•0.002
fri.,
+0.000•0.000+0.000•0.000+0.000-0.000+0.000•0.000.0.001-0.000+0.001-o.ooo+0.001•0.001+0.001•0.001+0.001-0.001
ör,.
+0.001•0.001+0.001-0.001+0.001-o.oot+0.002-0.001+0.003-0.001+0.003-0.001+0.004-0.001+0.005•0.001+0.008-0.002
är.
+0.003-0.001+0.004-0.001+0.004-0.001+0.004-0.001+0.005-0.001+0.005-0.001+0.006-0.001+0.007-0.002+0.009-0.002
6r„
+0.000-0.00!+0.000-0.001+0,000-o.oot+0.000-0.001+0.000-0.001+0.000-0.001+0.000-0.001+0.000-0.001+0.000•0.001
«>„+0.000-0-006
+O.OOO-0.006+0.000-O.OOfl+0-000-0.007+0-000-0.008+0.000-0.008+0.000-0.010+0.000-0.0 II+0.000-0.014
fr.+0.032-0.010+0.031•0.01 1+0.029-0.012+0-028-0-015+0.025-0.017+0-023-0,021+0.020-0,025
+0-0 M•0,031+0-005•0.044
Table C.l-1; The spin dcnsity matrix cicmcnt r°i, äs obtained from fits accordingto cquation (3.72) {uppcr tablc) and cquation (9.17) (Iower tablc) in \t\. Thesystcmatic crrors obtained for thc crror classes affccting the result are also given.
<,U„,„-) (G*V>
0.61 7
0.688
0.721
0.746
0.769
0.797
0.838
0.951
-0«rOO
0.030±0.0230.052±0.0310.008
±0.029-0.064±0.022-0.023±0.0160.016±0.024-0.00«±0.0190,062
±0.013
ü r,
-0.026-0.015+0.021-0012-t-0.019-0.01 1-t-0.018-0.010+0.016-0.009+0.0 H-0.008+0.011• 0.006+0.004-0.002
6r„
-0.009•0.008-•-0.008-0.007-0.007-0.007+0.007-0.007+0.007-0.007+0.006-O.OOT4-0.0060.006
+0.004•0.005
o'',,.
-0003• 0.005-1-0.003-0.004+0.003-0.004+0.002-0.004+0.002•0.004+0002-0.003+0.0020.003
+0.001•0.002
6r„
-0.002-0.001-0.002-0.002+0.002-0.002+0.002-0.002+0.002•O.OO2+0.002-0.003+0.002-0.003+0.002-0004
fl r.
+0.001-0.005+0.001-0.004+0.001-0.003+0.001-0.003+0.001-0.003+0.001-0.003+0.001-0002+0.001-0.001
6r„
+0.000-o.ooo+0.000-0.000+0.000-0.000+0.000-0.000+0.000-0.000+0.000-0.000+0.000-0.000+0.000-0.000
d>j.
-•-U. 003•0.003+0.003• 0.002+0.003-0.002+0.003-0.002+0.003-O.OO2+0.003-0.002+0.003-0.001+0.004-0.001
i».»0005-0.031-.0005-0.025+0.005-0.022+0.004-0020+0.004-0.019+0.004-0.016+0.004-0.013+0.003-0.004
(.U„,-}(GeV)
0.617
0.688
0.721
0.746
0.769
0.797
0.838
0.9S1
r0* roo
-0.053=0.0230.077±0.037-O.OOL±0.032-0.031±0.0330.004
±0.0260.028
±0.027-0.025£0.0190.070
±0.015
6r,
+0.006-0.017+0.006-0.016-O.OO6-0.016+0.006-0.016+0.006-0.015+0,006-0.015-0007-0.01S+0.007-0.013
ör„
+0.009-0.009+0.008• 0.009+0.007-0.008»0.007•o.ooa+0.006-o.ooa+0.006•0.008»0.0050.007
+0.003•0.00«
rfn,;
+0.007•0.007+00060.007
+0.005-0.006+0.005-0.006+0.005-0.006+0.004-0.006+0.004-0.006-0,002-0.005
6r„
-0.00!-0.008+0.001-0.005+0.001-0.005+0001-0.004+0.001-0.004+0.00 L-0003+0.002-0.003+0.002-0.00t
<ir.
+0.000-0.008+0.000-0.006-rO.OOO-0.006+0.000-0.005+0.000-0.005+0.000-0.004+0.000•0.003+0.000-0.001
Ar,.
+0.000-0.000+0.000-0.000+0.000-0.000+0.000-0.000+0.000•0.000+0.000-0,000-rO.OOO
-0.000+0.000-0.000
•»i.+0.001-0.004+0.00!-0.004+0.001-0.004+0.001-0.004
+0.001-0004+0.001-0.004+0.001-0.005+0.001-o.oos
6r,
-0.006-0.034+0010-0.028+0.012-0.025-0.013-0.023+0.0 U-0.021+0.01«-0.018+0.018-0.015+0.024-0.005
Tablu C.15; Likc table C.12 bui in M,*,- bins.
(A/..,-)(GeV) | Kr?3
0.617
0.688
0.721
0. 1 16
0.769
0.797
0.838
0.951
•0.034±0.0140.013
±0.016-0.012±0.01-1-0.018±0.01-1-0.007±00150.062
iO.QI3Q.02510.0110024
är\2
• 0.044+0.010-0.036-0.009-0.032-0.008-0.029+0.007-0.027+0.006
0.024+0.005-0.019-0.002
±0 008 ! -0.006
6r„
-0.010-0.003+0.00«-0.003-0.007-0.002-0.007•0.002-0.0060.002
+0.005-0.002+0.004-0.001+0.001-0.000
är-Ht
+0004-0.002-0.003-0.002+0.003-0.001+0.003-0.001+0.003•0.001+0.003-0.001+0.002-0.001+0.0020.001
•Sri,
+0.001-0.003-0.001-0.003+0.001•0.003t-0.001•0002-0.001-0.002+0.001•0.001-Ü.001-0.002•t-0.002•0002
dr.
-0.001-0.003-0.000-0002+0.000-0.002+0.000-0.002+0.000-0.002+0.000-0.002+0.000-0001+0000-0000
6r„
+0.000-0.000-0.000-0.000+0.000-0.000+0.000•0.000+0.000-0.000+0.000-0.000+0.000-0.000-0.000-0.000
Sr„
+O.OOO• 0.000-0.000-0.000+0.000-0.000+0.000-0.001+0.000-0.001+0.000-0.001+0.000-0.001+0.000-0001
<fr„
+O.O.W-0.003+0.041-0.006+0.036-0.006+0.033-0.007+0.030-0.008+0.027-0.009+0.021-0.010+0.0070.013
Tablc C.16: Likc tablc C.13 bin in -V/.*.- bins.
I.V2 ix C.'liibh-s uf Dutn
? 9 ? 9 ? 9 ? 9 ? <? ? '
8 § 8 g 8 § S g 8 g 8
? = ? 9 9 . 9 ? 9 ? o ? o 9 t ? ' J '
9,99.99. 99.99..
s^s|8l81> ° 9 ° 9 ? 9
85S'
S g S i
+ T1 + ^ + f 4
— S"3po=Ö°S°5og
O
U
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BIDUOGRAPHY
Danksagung
Es war eine interessante Erfahrung eine Doktorarbcit im Rahmen einer großen interna-tionalen Kollaboration anzufertigen- Während dieser Zeit habe ich sehr viel Unterstützungerfahren, die zum Gelingen der vorliegenden Dissertation beitragen hat. An dieser Stellemöchte ich mich für diese Unterstützung bedanken. Besonders danke ich:
Meinem Betreuer Robert Klanncr für die Möglichkeit in der ZEUS Kollaboration mitzuar-beiten und für seien Einsatz bei der Absicherung meiner wirtschaftlichen Lage über die langeZeit. Darüberhinaus habe ich in zahlreichen Diskusionrn und durch viele, meißt nützliche,Anregungen zur Analyse viel von Ihm gelernt.
Heiko Bcicr, Jörn Grossc-Knetter, Alexander Proskuryakov, Mirhal Kasprzak, Luciano Lam-berti und Roberto Sacchi danke ich für die gute Zusammenarbeit. Ich habe an verschiedenenStellen in meiner Analyse von Ihren Arbeiten profitiert und Ihre Diskusionsbercitschaft oftund gerne genutzt.
Allen Koordinatoren der Soft Photoproduction und Diffraction working group danke ich fürdie zahlreichen Anregungen. Insbesondere Burkliard Bnrow und Michclc Arneodo haben dieEntwicklung dieser Arbeit kritisch begleitet und unterstützt.
Für die Durchsicht des Manuskripts und die konstruktiven Anregungen danke ich Prof.Lohrmann. Sampa Dhadra und Durkhard Burow haben durch ihre kritische Durchsicht desManuskripts dafür gesorgt, daß der englischen Sprache kein allzu großer Schaden /ugefügtwurde.
Schließlich danke ich allen Doktoranden und Diplomanden die mir meine Zeit bei DESYdurch allerlei kurzweilige Gespräche, nicht nur über Physik, verkürzt haben. Besondershervorheben möchte ich: Martin Löwe, Heiko Beter, Kars ührenbcrg, Kai Desler, TeresaMontciro, Jörn Grossc-Kncttor, Song Ming Wang, Jason McFall, Olaf Deppe, Bernd Surrowund Joachim Stamm.
Abschließend möchte ich meiner Frau Utr und meiner Familie für die Geduld danken die Sieaufgebracht haben. Ihnen und nieinen Freunden und Bekannten habe ich dafür zu danken,daß Sie mir immer wieder vor Augen gehalten haben, daß es ein Leben außerhalb des DESYgibt.
